Federalism is the shared governance of a territory, in the United States federalism is divided into three parts: local, state and national governments. Federalism is evolving relationship between governments and has been evvolving since the founding of the U.S.A.
In general, there are two forms of federalism:
Dual Federalism- local, state and national government have separate mandates to accomplish common goals. Consider law enforcement, most place in America are protected by local police, state police, and federal law enforcement (FBI, ATF, Homeland Security).
Cooperative Federalism- local, state an national government have common mandates. Local, state and federal governments cooperate to have schools and share funds to provide for education.
There are many other types of federalism, dual and cooperative are considered the most recognized definition.
Federalism in America