A Capitol, often abbreviated as "Cap", is one of the most important buildings in the game. In random map games, it is the starting core of each player's base. You start with a capitol and some citizens (anywhere from 1 to 20, depending on the settings). The capitol makes units such as citizens, heroes, and canine scouts. It also provides research for different technologies (depending on the epoch) which can aide the player in the future. The capitol can also research the next age when it's available.
A player can make several capitols, but one may only actually be built when the player does not already have a Capitol or Town Center. After that, in order to get a capitol a player must first populate a Settlement into a Town Center with five citizens, and then again populate that Town Center into a capitol with an additional ten citizens.
A capitol can also provide morale up to a certain distance, which is denoted by the blue/green line that appears on the terrain when the capitol is selected. The article on morale provides more details on how morale works.
Your capitol is also a resource drop point, like Settlements and Town Centers. Town Centers and Capitols provide a gathering bonus when they are built next to a stone, gold, or iron mine. This bonus does not apply to food or wood sources. The gathering bonus comes in the form of additional resources when a citizen drops them. For example, when a citizen drops 15 iron at a nearby capitol, you will gain a 7 iron gathering bonus (50%, rounded down), for a total of 22 iron that is added to your available resources. This bonus can be increased by populating additional citizens at a capitol, up to 50 for one building (35 additional). A fully populated capitol yields a 100% bonus, doubling the amount you gather.