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I think your asking "What are concurrent powers". The answer is that they are powers shared by the federal government and the state governments
Concurrent powers of the individual states and federal government: Power to (1) tax (2) establish a standing army - military/national guard (3) legally adjudicate in courts of law (4) convict and hold people in jail/prisons (5) build and maintain roads (6) hold elections You're Welcome
I believed they are shared between state and local governments
This concept is known as federalism. The United States and Canada are two example countries that employ this form of government. The European Union is also sometimes recognized as a federalist system, although to a different extent.
Powers shared by both the federal and state governments are called "concurrent powers." For example, they both have the power to tax, to try criminals in court, and to build roads.