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.