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 also the most glorious and productive city in your empire. The first city you settle will automatically become your capital in the beginning of the game, and is also considered your "Original Capital" for the purposes of a domination victory.
You can connect other cities to your capital to form the internal trade network of your empire, using the appropriate infrastructural connections. These links are called trade routes (or City Connections in Brave New World). Each connected city will then generate Gold each turn thanks to trade, which will be applied straight to your treasury for purposes of local Gold-boosting buildings.
Only players in control of their original capitals are eligible for a domination victory.