Your capital is a colony that you designate to be your main colony by clicking the "Establish Capital" button. There is no default capital so you have to establish one to get the benefits. There is a 30 day wait after setting up a capital before it is officially set up and doing anything. After that, it increases in effectiveness through 4 levels. Those levels are indicated by a text title. (New Capital, Growing Capital, Thriving Capital, Established Capital).

Essentially, your capital is a statement. In additions to its role in religious empires, your people will also defend it very vigorously. When trying to conquer a capital, be ready to face serious civil defenses.

Capital Colonies show up in yellow in your list of colonies. There is also an option on the settings page to have your capital at the top of the list.