Powers of government that are reserved for states sometimes referred to as "state's rights" (often in the context of opposition to civil rights.) It basically gives the individual state the right to determine its own local government and policy on issues (health, safety, etc.) that fall outside of the broader definitions of federal law. It's like micro marketing for legislation. The exception to this is that local laws cannot directly conflict with federal law.

A perfect example of this is Little Rock's refusal to integrate its schools which led to direct intervention (and occupation) by federal troops to make sure the law was followed.