This is an attempt to do a writeup of everything you'll need to know to make a character and play in this campaign. It's not an exhaustive list, and it's not stuff every character will know, although they'll know most of it. But it should give you a feel for the basic vibe, geography, and history of the campaign.
Like most D&D campaigns, Eberron is set among the ruins of a fallen empire, that once spanned the continent and had some magic items and stuff, and is now no more. Unlike most D&D campaigns, the empire fell just a century ago, and people were still fighting over the remains until a good two years ago. The vibe here is post-WWI, with all these soldiers back from the war and not sure what to do, the different countries in an uneasy peace and eyeing each other suspiciously, and all these weird magical weapons having been developed and people talking about how war will never be the same again.
But it's also got all the crazy pulp-action stuff you expect from the 1930s: south of the main continent of Khorvaire is the jungle continent of Xen'drik, covered in ruins from mysterious ancient civilizations, prowled by sinister dark elves riding scorpions and armed with wicked metal boomerangs. And even weirder stuff. Back on Khorvaire, there's the Lightning Rail, a magical train whose coaches levitate above the tracks so it can zip along, and fire-elemental-powered airships that soar high in the sky. If you think you may end up fighting on at least one of these while the vehicle is in motion, you are probably correct. There are mad cultists of The Dragon Below who plot sinister schemes of chaos, and at least a half-dozen other groups seeking world domination. And don't even get me started on the crazy wizards who study the planes as they shift in their transdimensional orbits, waiting for the right conjunction to power their infernal machines.
Another important thing about Eberron is that it's partly an attempt to extrapolate a world where you have low-level magic available on a large scale. In a not-too-shocking turn of events, it ends up replicating a lot of technology: besides the aforementioned train and zeppelin-analogues, you have magical lamps on the streets of the big city, magewrights working on crafting fine items and breeding magical animals, and then there's all the stuff that got built for the war. Most notably, the warforged: these guys are like intelligent golems made from living wood and metal, created to be the perfect soldier. For the entire war they were considered to be slaves or property, but part of the armistice agreement gave them full citizenship rights and stuff. This doesn't mean that the average guy on the street accepts them, though.
Finally, the last thing to know is about dragonmarks. See, in Eberron you have the countries that are, obviously, important entities. But almost as important are the twelve Houses. Each House is mostly run by a very large extended family. Why? Because the power of the House comes from dragonmarks — mysterious symbols that some people are born with, and get passed down erratically through family lines. People with those symbols have the intrinsic ability to use certain magic powers — people with the Mark of Healing can heal wounds and cure diseases, and people with the Mark of Storm can control the weather.
The Houses have parlayed these powers into various guilds, which in turn have enormous influence across the continent. For instance, House Jorasco's Mark of Healing let them start the Healer's guild, which runs virtually all the hospitals. House Orien's Mark of Passage gives them the guilds of Couriers and Transportion, and if you want mercenaries you talk to the folks with the Mark of Sentinel. Obviously, there are healers who don't belong to House Jorasco (clerics, for instance), but Eberron doesn't have a lot of high-level characters (like, a quarter or fewer of what a standard setting has), so the powers of the House dragonmarks makes them like IBM or US Steel (and there's been no trust-busting attempts, at least not yet). Note that not everyone in a House has a dragonmark: there's plenty of room in the House for administrators, diplomats, bookkeepers, janitors, and so on, depending on your other talents.
Most of the races in Eberron have the same general flavor as the standard one, but there are enough exceptions that it's worth giving a quick run-down. In addition, dragonmarks are race-specific, so I'll note which have which.
Humans: Humans are, as usual, the majority race and run most of the kingdoms created as a result of the Last War. Humans can have the Mark of Finding, the Mark of Handling, the Mark of Making, the Mark of Passage, and the Mark of Sentinel.
Half-Elves: Half-elves, also as usual, are kind of ill-defined and are basically humans with pointy ears. But they do have two cool dragonmarks: Detection and Storm.
Half-orcs: Unlike the vibe in standard D&D, half-orcs in Eberron are the remnants of an ancient empire. They tend to be primitive but in a noble-savage kind of way: many are druids, and it was only through their efforts that an incursion by weird creatures from another plane was fought off centuries ago (too bad nobody besides a few druids still remembers this). Some half-orcs these days live in the frontier kingdoms, living a prospector's or trapper's lifestyle: this is made easier for them because they can have the Mark of Finding.
Halflings: There are two kinds of halfings in Eberron. There are the ones that live in the cities. These are pretty similar to standard D&D: some are a little rogueish and sneaky, some are nice and hospitable (the second type is even the more common, as their marks of Healing and Hospitality let them run inns and waystations). Then there are the wild halflings. They live out in the desert, tame dinosaurs to ride, and are masters at setting up ambushes for their prey. Yeah. So before you mess with a halfling, better find out how long it was since he came from the desert.
Gnomes: Gnomes in Eberron look short and cute and big-nosed and adorable, just like in standard D&D. They make themselves useful at banks and libraries and museums with the Mark of Scribing, and hardly anyone thinks an unkind word about them. Which is just how they like it. Because you know how the Gnomes of Zurich live in Switzerland and are the Illuminati-like secret masters of the world through their control of finance and agents in every government and organization? That's these guys. The tiny gnome kingdom of Zilargo is thick with conspiracy, treachery, political maneuvering, and backstabbing. Outsiders who come in are unlikely to see any of it, and just go away thinking how clean and safe all the streets are. But that doesn't mean it's not there. Oh, the gnomes are also masters of elemental binding, so they have enormous political leverage by being the only ones who can power the airships to make those fly (although it takes a half-elf with the Mark of Storm to steer one).
Elves: There are basically three kinds of elves in Eberron. There are the ones with the Mark of Shadow, who belong to either of the two guilds that specialize in entertainment, storytelling, acrobatics, music, and spying. There are the ones that live on Aerenal, the island over the sea, where they are rumored to be ruled by an Undying Court of the most revered ancestors — or perhaps this is just rumors caused by their reverence of their ancestors, study of history, and obsession with death. Finally, there are the crazy warrior elves, who decided to stake out a claim on the main continent for themselves during the Last War, and like nothing better than drawing swords and riding out on horseback to defend it.
Dwarves: Dwarves live in various holds in the mountains, you will be surprised to hear. Their Mark of Warding lets them run guilds specializing in banking and defense, and naturally they also do extensive mining and smithing on the side.
Changelings: This crossbreed of doppelgangers and humans is now a true-breeding race in its own right, although it's pretty similar to both parents. They're generally found as rogues, unsurprisingly, though they're as adaptable as humans. Their main shtick is to be able to do a Disguise Self thing at will. Changelings never have dragonmarks.
Kalashtar: This is a psionic race, but I think I'm going to skip psionics for this game, so these guys are out.
Shifters: Like changelings, shifters are a crossbreed, of lycanthropes and humans. They have the power to shift into a crossbreed form — maybe growing razor claws, or a tough hide, or being able to make huge leaps — a few times per day, with it getting more powerful as they spend more feats on it. They tend to be rangers or other wild/frontier things, and never have dragonmarks.
Warforged: These guys are the weirdest of the new races, and are basically like living, intelligent golems. They don't need to eat or sleep or breathe (although they still have to rest before memorizing spells). Curing spells only have a partial effect on them, and there's a different set of repair spells that work instead. The oldest warforged is only like 15 years old, as they were all built during the Last War to serve as troops, using special magical creation forges (although interestingly, there are some signs that warforged-like artifacts have been found on the southern continent — could the creation forges have been secretly developed with magic found there?). Discrimination against warforged is still pretty widespread: although the treaty ending the Last War gave them full citizenship rights in all the signatory countries, that doesn't mean the average person doesn't still think they're hella creepy.
There's one new class, but almost all the standard classes are exactly the same. Here are a few notes anyway, though.
Artificers: Artificers specialize in making items, magic and non. They can't cast any spells, but they can infuse items with power temporarily, or spend more time to make a permanent magic item. They have the ability to fiddle with traps and other devices just like thieves do, and have enhanced abilities to work with magic items. This is a new class for the setting, and I can provide more information about it if desired.
Clerics: Clerics can choose to worship the Silver Flame (the national church of one of the countries, it's sometimes accused of bordering on the inquisitorial, especially in reference to the great lycanthrope purge of 50-odd years ago), the Blood of Vol (if they're from Karrnath), the Sovereign Host (a general pantheon of nine gods worshipped by most everyone else, unless they're a cultist), or a specific god in the Sovereign Host. Note that in Eberron, clerics can be of any alignment — the gods don't interfere with daily life and don't send down visions, so there is nothing to prevent a cleric from being overzealous and shifting into evil behavior). Here's a good post on enworld talking more about religion in Eberron.Druids: Druids go way, way back. In olden days they were defenders of the world against creepy things from other dimensions. These days they've factionalized to a certain extent, and no longer present a united front. Here are some of the larger sects:
Monks: Monks can take feats to let them multi-class normally, and use a few other snazzier weapons as monk weapons.
Paladins: Halfling paladins can ride dinosaurs for their special mount, of course.
Rangers: Some rangers are associated with the druidic sects mentioned above. The same rules on animal companions apply also.
One of the shticks about Eberron is that it's intended to be more morally ambiguous than the standard D&D setting, and this obviously has potential conflicts with D&D's absolutist alignment system. The minor resolution to this is to get rid of fixed monster alignments: in Eberron, you may well run into lawful good orcs, chaotic evil gold dragons, true neutral mind flayers, and so on. People don't necessarily stereotype based on race — but if all the hobgoblins someone encounters are bandits, they may well have an "hobgoblin = bandit, shoot on sight!" mentality. On the other hand, they may feel the same way about humans from Aundair. This applies only to creates native to Eberron, I should mention — iconic extraplanar creatures like angels, devils, and elementals all retain their usual alignments 100% of the time.
The major fix to alignment is this: evil people are not necessarily bad people to interact with. Furthermore, there are a lot more of them in society than in many standard D&D settings. The innkeeper who shorts her customers, the gate guard who takes bribes to let smugglers in, the club owner who knows the club is a hangout for criminals but leaves it open because it's profitable — probably all evil. Anyone who is strongly self-interested, to the point where other people are harmed by it, is probably evil. In addition, anyone who resorts to bad means to achieve their ends, even if they're good ends, is probably evil: a crusading priest who'll go to any length to weed out the heretics, a mage who sacrifices innocents for his experiments to find the cure for some horrible disease, an intelligence operative who tortures the terrorists to find out where they're planning on striking next.
The upshot is that there are lots of evil people, and many of the evil people may be quite nice in some respects. Magic to detect evil exists, but it's certainly not proof of anything. In some cases it won't even work — undead always radiate an evil aura (in addition to whatever "real" alignment they have), and clerics always radiate an aura of whatever deity they worship.
It may be useful to look at this good-sized map of Khorvaire and the wikipedia entry for Khorvaire. Also, note that the original empire that was broken up by the Last War was named Galifar, and had Aundair, Thrane, Breland, Cyre, and Karrnath as its core — these are still called the Five Nations.
Aundair: Aundair is a human kingdom ruled by Queen Aurala. It has a long tradition of knowledge, magical study, art, and wine-making. It's often considered to be the most cultured place on Khorvaire, and the queen considers this ample evidence that it should rule the new empire when it inevitably reforms. During the Last War Aundair used a lot of mercenary troops, and is probably working on amassing them again privately, even as the Queen tries to keep on peaceful terms with her neighbors to keep things quiet for now.
Breland: Breland is a human kingom ruled by King Boranel, although he has delegated a lot of power to advisors and the kingdom may theoretically turn into some kind of democracy. It's a big center of industry, and was one of the heaviest users of warforged troops during the war. Breland has opened up their gates the widest to refugees from Cyre, and this kingdom is generally presented as the good guys, although this doesn't mean they don't have an extensive espionage network, guard patrols, and occasional border scuffles.
Karrnath: Karrnath is a human kingdom ruled by King Kaius III. They're infamous for using undead troops during the war — the Blood of Vol developed spells for raising soldiers as skeletons and zombies and sending them out to fight again. Despite this, the country's pretty nice, and a good place to go for military training, ale, or cheese. The vibe here is probably post-war Germany, where the population feels a mix of pride and shame about their past, and there's a long tradition of military stuff.
Mournland: Formerly Cyre, the Mournland is what's left behind when there is a crazy magical holocaust that wipes out an entire kingdom. Nobody knows who or what caused it, they just know the entire place is blasted scrubland, no wounds heal, the land is covered in mass graves and ghost cities, and weird magical effects and mutated monsters wander the area (and occasionally out of it! Sucks to be Thrane and Karrnath). The few Cyre folks who survived have settled elsewhere; some still talk about rebuilding.
Thrane: Thrane is your basic stick-up-their-ass Lawful Good human theocracy. The Church of the Silver Flame is the official state church, and the head of government is its high priestess, even though she's only eleven years old. Thrane is industrious, prosperous, and irritating to its neighbors. During the war they used mostly mercenaries and homegrown troops, and many people still feel that Thrane used the war as an excuse to try to spread its faith to other countries. Thrane tries to be as self-reliant a country as possible, and interacts the least with the Houses.
Eldeen Reaches: Mostly forest and plains, this kingdom is pretty loosely governed, and hence is a popular place for druids and rangers. There are also a lot of animal breeders here for obvious reasons. It's one of the new ones since the war — it used to be part of Aundair, but split off less-than-amicably.
Shadow Marches: The Shadow Marches are like the Eldeen Reaches, only with swamps. This kingdom has the largest half-orc population on the continent, and it's no surprise that the Mark of Finding is primarily based here. This is convenient, since the Shadow Marches is also one of the best places for prospectors dragonshards, magical crystals that have many uses for crafting and magic.
Lhazaar Principalities: This kingdom is really a loose collection of sea lords, most of whom are at least half pirate. There is a lot of internal feuding, but it doesn't usually keep them from preying on neighboring ships. Unsurprisingly, there's a certain rivalry between them and the Houses that focus on travel and transport.
Mror Holds: These are the holds where the dwarves live. There are rumors of things deep within the earth, and one now-abandoned hold, sealed off for centuries for reasons no one is exactly sure of. One hold draws its power from the Fist of Onatar, a still-active volcano that gives its forges amazing power.
Q'barra: This is a mostly-jungle nation home to all sorts of survivors. The first people who came here were the ones who refused to participate in the Last War because they felt more loyal to the empire as a whole than to any country. Then later there were people who lost their homes to the Mournlands, and people who couldn't fit in at home after the war for other reasons. It's very sparsely settled — there are only two major cities. At least, it's very sparsely settled by humans: who knows what could be lurking in the jungle, but there are rumors of great lizardfolk civilizations.
Talenta Plains: These open plains are where the wild halflings live their nomadic lifestyles, and dinosaurs roam. Travelers are advised not to wander around without a guide, or some hunks of meat to distract hungry dinosaurs.
Valenar: This is the chunk of land claimed by warrior elves during the Last War. It is primarily open plains on which they ride and breed their horses, but there are also areas of forest, desert, and so on.
Zilargo: This is where the gnomes live. It is much like Switzerland, although with bound elementals instead of cuckoo clocks. The city of Korranberg is home to the Library of Korranberg, the largest library in the world, and to the Korranberg Chronicle, the most popular newspaper on Khorvaire.
Darguun: This is the remains of the ancient hobgoblin kingdom. We're probably not going to focus on it, but it's a good place to hire mercenary troops.
Demon Wastes: This is like a slightly less weird, but no less dangerous, version of the Mournlands. It's mostly desert, plains, and steppes, supposedly inhabited only by nomadic barbarian tribes who practice strange rituals. So why is it called the Demon Wastes, then?
Droaam: This is the kingdom where all the monsters live. You got your mind flayer, you got your hill giants, you got your harpies, you got your trolls. This is stupid and we will be pretending it doesn't exist.
This lists off the twelve different dragonmark houses, and what their powers are. Some claim there was a thirteenth dragonmark house which possessed the Mark of Death, but if such a thing once existed, someone must have gone to great effort to try to wipe out every trace of it.
Having a dragonmark implies that you belong to a dragonmark house and are descended from someone else with that same dragonmark (though the reverse isn't true — probably 20% of the people in a house have a dragonmark, with least:lesser:greater in a 100:10:1 ratio). If you have a dragonmark, you can always get a job via the house if you want one, although what job it is will depend on your personal talents as well as the power of the mark (House Sivis will pay someone with the Mark of Scribing a gold piece a day to sit in a room in some village in the middle of nowhere every day and transcribe and pass on any messages that come in).
From a game-mechanics perspective, there are three dragonmark feats to take. You must take the earlier ones before taking the later ones. Each one lets the character use a certain spell as a spell-like ability at a certain caster level. Many dragonmarks list a few choices for spells; in this case, you have to pick one when you take the feat and can't cast the others. Like any spell-like ability, the DC for powers which allow saves is 10 + the character's charisma modifier + the spell level. Conveniently, dragonmarks may manifest at different times in different people's lives, so you're not required to take the feat at 1st level.
Mark of Detection: The half-elves of House Medani run the Warning Guild, which offers services relating to personal protection and detection. They act as scouts, food-tasters, sentries and detectives.
Least Mark: detect magic 2/day or detect poison 2/day; +2 to Spot checks
Lesser Mark: detect scrying 1/day or see invisibility 1/day
Greater Mark: true seeing 1/day
Mark of Finding: The humans and half-orcs of House Tharashk run the Finders Guild, which offers services relating to location and retrieval. They act as prospectors, bounty hunters, and investigators.
Least Mark: identify 1/day, know direction 2/day, or locate object 1/day; +2 to Search checks
Lesser Mark: helping hand 1/day or locate creature 1/day
Greater Mark: find the path 1/day
Mark of Handling: The humans of House Vadalis run the Handlers Guild, which offers services relating to animal breeding, training, and animal byproducts. They act as ranchers, breeders, coachmen, trainers, tanners, and so on.
Least Mark: calm animals 1/day, charm animal 1/day, or speak with animals 1/day; +2 to Handle Animal checks
Lesser Mark: dominate animal 1/day or greater magic fang 1/day
Greater Mark: animal growth 1/day or summon nature's ally V 1/day
Mark of Healing: The halflings of House Jorasco run the Healers Guild, which offers curative services of all kinds. They run hospices across the continent, and have a sideline in alchemy.
Least Mark: cure light wounds 1/day or lesser restoration 1/day; +2 to Heal checks
Lesser Mark: cure serious wounds 1/day, neutralize poison 1/day, remove disease 1/day, or restoration 1/day
Greater Mark: heal 1/day
Mark of Hospitality: The halflings of House Ghallanda run the Hostelers Guild, which covers inns, hotels, restaurant managers, chefs, and so on.
Least Mark: purify food and drink 2/day, prestidigitation 2/day, or unseen servant 1/day; +2 to Diplomacy checks
Lesser Mark: create food and water 1/day or secure shelter 1/day
Greater Mark: hero's feast 1/day or mage's magnificent mansion 1/day
Mark of Making: The humans of House Cannith run the Tinkers Guild, members of which tend to be nomadic and offer services relating to repair. House Cannith also runs the Fabricators Guild, one of the most powerful guilds on Khorvaire, which creates and improves new items rather than repairing old ones. They act as architects, construction supervisors, and craftspeople of all types.
Least Mark: make whole 1/day, mending 2/day, or repair light damage (like cure light wounds, but for constructs) 1/day; +2 to Craft checks
Lesser Mark: minor creation 1/day or repair serious damage 1/day
Greater Mark: fabricate 1/day or major creation 1/day
Mark of Passage: The humans of House Orien run the Couriers Guild, which delivers messages all across Khorvaire, and the Transportation Guild, which delivers people — this latter oversees the Lightning Rail and more mundane caravans.
Least Mark: expeditious retreat 1/day, mount 1/day, or dimension leap 1/day (teleport yourself up to 10 feet per level); +2 to Survival checks
Lesser Mark: dimension door 1/day or phantom steed 1/day
Greater Mark: overland flight 1/day or teleport 1/day
Mark of Scribing: The gnomes of House Sivis run the Speakers Guild, which offers services relating to translation, mediation, and long-distance real-time communication. They also run the Notaries Guild, which both certifies documents and helps secure them. They generally work in banks, libraries, and governments.
Least Mark: arcane mark 2/day, comprehend languages 1/day, or whispering wind 1/day; +2 to Decipher Script checks
Lesser Mark: illusory script 1/day, secret page 1/day, or tongues 1/day
Greater Mark: sending 1/day
Mark of Sentinel: The humans of House Deneith run the Blademarks Guild, which provides mercenary services, and the Defenders Guild, which offers comprehensive bodyguard services. Control of the Blademarks Guild made Deneith extremely powerful during the Last War.
Least Mark: mage armor 1/day, protection from arrows 1/day, shield of faith 1/day, or shield other 1/day; +2 to Sense Motive checks
Lesser Mark: protection from energy 1/day or lesser globe of invulnerability 1/day
Greater Mark: globe of invulnerability 1/day
Mark of Shadow: Elves with the Mark of Shadow actually fall under two houses, House Phiarlan and House Thuranni. The split is more for political reasons than practical ones — probably schizophrenia caused by trying to sell spying services to every country involved in the war at once led to internal conflict over what was best for the House. Members of both Houses have the same powers, and act as entertainers, storytellers, musicians, acrobats, spies, and information brokers, given that those with the mark have powers relating to both divination and illusion.
Least Mark: darkness 1/day, disguise self 1/day, or minor image 1/day; +2 to Gather Information checks
Lesser Mark: clairaudience/clairvoyance 1/day, shadow conjuration 1/day, or scrying 1/day
Greater Mark: mislead 1/day, prying eyes 1/day, or shadow walk 1/day
Mark of Storm: The half-elves of House Lyrandar run the Windwrights Guild, which dominations transportion over sea and sky, and the Raincallers Guild, which provides vital services to farmers. Their mark gives them power over winds and weather.
Least Mark: endure elements 1/day, fog cloud 1/day, or gust of wind 1/day; +2 to Balance checks
Lesser Mark: sleet storm 1/day, wind's favor 1/day (create a 30mph wind in a 10x10x100-foot volume, for 1 hour/level), or wind wall 1/day
Greater Mark: control winds 1/day or control weather 1/day
Mark of Warding: The dwarves of House Kundarak control the Warding Guild, which offers secure keeping of items and protection for the home. They work as bankers, guards, security consultants, and locksmiths.
Least Mark: alarm 1/day, arcane lock 1/day, firetrap 1/day, or misdirection 1/day; +2 to Search checks
Lesser Mark: explosive runes 1/day, glyph of warding 1/day, or nondetection 1/day
Greater Mark: mage's faithful hound 1/day, greater glyph of warding 1/day, or guards and wards 1/day
Aberrant Marks: A very few people are born with an aberrant mark, that belongs to no recognized house. This is generally caused by marked members of two houses having a child, and is frowned on by those who have heard of it (most people haven't, although there was a nasty war about it centuries ago). Usually people with aberrant marks don't belong to a dragonmark house, though it's possible, as long as they haven't manifested a "real" dragonmark.
Aberrant Mark: burning hands 1/day, cause fear 1/day, charm person 1/day, chill touch 1/day, detect secret doors 1/day, feather fall 1/day, inflict light wounds 1/day, jump 1/day, light 1/day, pass without trace 1/day, produce flame 1/day, shield 1/day, or floating disk 1/day
Aberrant marks act like normal dragonmarks, mechanically. They cost a feat which can be taken at first level. There is no "lesser" or "greater" version of an aberrant dragonmark. Races which can't have a normal dragonmark can't have an aberrant mark. Unlike normal dragonmarks, the caster level for an aberrant mark is equal to half the character's level, not a fixed number.