What powers are reserved for state governments?
When the Constitution was written, the Framers granted, or delegated, certain powers to the national, or federal government. These included such powers as regulating interstate commerce, printing and coining money, declaring war, and so on. It was generally agreed that those powers not delegated by the Constitution to the federal government would be reserved to the states. The Tenth Amendment, ratified with the rest of the Bill of Rights in 1791, made that agreement a guarantee by stating that all "powers not delegated to the United States by the Constitution, nor prohibited by it to the states, are reserved to the states respectively, or to the people." So if a power is not granted to the federal government, and if its exercise does not run counter to the Constitution, then it is reserved to the states.
In practice, this includes such powers as licensing, regulating and providing for public education, making state highway laws, and other things that are clearly best left to state governments. But the proper relationship between federal and state government, and the extent of reserved and delegated powers, remains a contentious one. Just today, several state governors are asserting the power to regulate immigration by refusing to admit Syrian refugees. Since Congress alone is empowered to regulate immigration, this could raise an important constitutional issue.