The seat of government is (as defined by Brewer's Politics) "the building, complex of buildings or the city from which a government exercises its authority".
The national government is usually located in the capital. In most countries, the capital and the seat of government are the same city; for example, Ankara is both the capital and seat of government of Turkey. London is additionally the capital city of both England and the United Kingdom, seating the UK's government.
The terms are not completely synonymous, as some countries' seat of government differs from the capital. The Netherlands, for example, has Amsterdam as its capital but The Hague is the seat of government.
Local and regional authorities usually have a seat (administrative centre) as well.