administrative jurisdiction or subdivision in any of various countries

A prefecture is a word used by countries such as Greece and Japan (called νομός, nomós in Greece and called ken in Japan). It is a smaller part of a country with its own government. It is a kind of local government.

Prefectures of Greece.

It is like an American state or a British county.

In France, it is the head of the department (see Prefectures in France for more detail).