Typical powers of a national government include defense and foreign affairs, currency, trade and immigration, and often taxation and major public services. In unitary states it usually also controls local government; in federal states its powers are shared with state or provincial governments.
Different countries use different terms: “central government”, “federal government” (in federations such as the United States, Germany or Australia), or simply “the government”. How much power the national level should have compared with regions and localities is the core question of the Federal vs Unitary axis.