Pirates of the Cursed Seas contains ten different nations. Nations in Pirates is very similar to civilizations in Age of Empires; they all more or less have the same things to offer, but have different focuses and bonuses. I will present to you the nations in the order of their appearance, beginning with the original set, Pirates of the Spanish Main.
Pirate - What would a pirate game be without, well, Pirates? Historically, pirates attacked ships and pillaged their loot. The same is true here: Pirate ships tend to be quick and boarding-oriented.
Spain - Spain is known for its gold. Again, they are fairly well represented in the game. Of all the nations, they have the most abilities that increase the value of gold dropped off at home, or otherwise increases gold-running potential.
England - The most powerful navy in the Age of Sail, England is full of warships. England is all about taking control; shoot first, ask questions never.
France - Introduced in the second expansion, Crimson Coast, France seems to prefer the blade over black-powder. While they aren't too bad in ship-to-ship combat, they seem to favor boarding strategies.
America - Introduced in the third expansion, Revolution, America brought with it a fleet of ships even more combat-oriented than England. They tend to be a little pricey as well. It's difficult to find a decent gold-runner for an America-pure fleet, but they are there.
Barbary Corsairs - Introduced in the fourth expansion, Barbary Coast, the Barbary Corsairs are a one-expansion wonder. Their entire armada consists of galleys, which are the epitome of boarding ships, because they can't be pinned. They also have the absolute worst cannons in the game; they are the only nation with rank 6 cannons. Boarding and gold-running are all the Corsairs are good for.
Jade Rebellion - Introduced in the fifth expansion, South China Seas, the Jade Rebellion are, you guessed it, an oriental nation. They exist only within this expansion. They introduced Chinese junks and Korean turtle ships to the game. They play really well either offensively or defensively.
The Cursed - Introduced in the sixth expansion, Davy Jones' Curse, the Cursed are the hardest nation to play with. Players of the Cursed should understand that the Cursed don't care about gold; they prefer to kill and have lots of abilities designed specifically for this purpose. For this reason, the Cursed is really more for fun than competitive play. The biggest appeal of the Cursed is the introduction of sea creatures to the game.
Mercenary - Introduced in the seventh expansion, Mysterious Islands, Mercenaries were introduced to play just that role. A lot of players try to play with them as a nation-pure fleet, but that is not at all the way to play (in that capacity, they play a little worse than the Cursed, considering they can't even dock at their own home island). The Mercenaries introduced submarines to the game, which made excellent battering rams, since they can ram while submerged.
Viking - Introduced in the eighth expansion, Frozen North, the Vikings were the last nation to be introduced and exist only within this expansion. They introduced viking longships to the game, as well as icebreakers. They pack a lot of punch, but can't take it in return. They are also fairly expensive, and don't play well at all in a standard game of 40 points. The Vikings excel at boarding and combat.
There are five mainstream nations in the game: Pirate, England, Spain, France, and America. While each of them have their focuses, they have enough variety among game pieces that they can do well with most any play-style, including combat, gold, and boarding strategies. The descriptions listed listed above are a general idea of what a majority of their abilities seem to focus on.