Your Capital is the city that contains your Palace, the center of your empire and your power as ruler. As the capital is your civilization's first and greatest city, it is usually the most glorious and productive city in your empire, and a conqueror's greatest prize!
The first city you settle will automatically become your Capital at the beginning of the game, and is also considered your "original capital" for the purposes of a Domination Victory - to win in this manner, you must control both your original capital and all other players' original capitals. If your capital is captured, the Palace (as well as the Capital status) will move to your next largest city.
In addition to the bonuses it receives from the Palace, the Capital is the only city that benefits when you have 1 or 2 Envoys at a city-state. There are also some Policy Cards, such as God King, Colonial Offices, and Colonial Taxes, that affect either the Capital or cities located on a continent different from the Capital's continent.