Your country's capital is placed when you join a world and cannot be moved. Your capital (or any capital you capture) can always be used to build a land base.
In a normal game in which players earn income from raw materials in each cycle, any player who doesn't control his capital has his income cut in half each cycle. In a game with no cycle income, any player who doesn't control his capital will lose 10% of his/her country funds each cycle.
Controlling an enemy capital doesn't give any bonus to the conqueror.