A Capital is a castle like your main castle. You can capture it the same way you would capture an Outpost. You don’t need a Castellan for capturing a Capital, because the system automatically provides you an extra, for this task.
The Capitals were mainly introduced into the game to bring a long awaited challenge for the (large) alliances. The number of Capitals is based (similar to the number of resource villages) on the number of players in the game world. The more players there are in a world, the more Capitals there are! Still the numbers are limited because the Capitals are “end game content”. This means that they are only meant for the strongest players and alliances.
If someone holds a capital in Great Empire,and builds a palace, then all the members of his alliance can recruit kingsguard units:
If someone holds a capital in Everwinter Glacier, Burning Sands or Fier Peaks and builds a palace, then all the members of his alliance can recruit renegades. The recruitment of these troops will be paid for with the respective resources of the Kingdom (coal, oil, glass). However, the acquisition is still much cheaper than the exchange in the local village.
You can see two spy reports of capitals: