One city per county is designated as that country's capital city. Capital cities can be attacked and conquered like any other city. If your city is a capital city you get additional bonuses (tap on a capital to find out what its bonuses are).

 

In addition to bonuses for the capital owner, they and their alliance collect Silver Tax from every trade made in any county they have a capital city in.

 

Counties are grouped into States, and States are grouped into Regions. Look out for these State and Region capital cities, they have particularly large bonuses for their owners.