A federation is a union of a number of self-governing states or regions, which are joined together under a central government. The central government is not able to do a lot of things that central government in more centralized states can. These things are done by the states (or regions) in a federalized state.
The United States of America is a federation. The federal (central) government has the highest executive role, but the states have their own special rules in some special cases.
Australia became a Federation in 1901.