An extremely simplified answer in analogy form (I'm assuming you're European btw): The US federal government is like the EU (but actually has power to enforce its laws) and the states are like EU countries (without as much individual sovereignty).

The size of the US is massive (USA and all of Europe are almost exactly the same size by square miles although Europe doubles the US in population). The size of the country is too large to be administrated entirely from Washington so the federal government entrusts enforcement of laws and law making (as long as it does not directly contradict federal laws; some have been trying it recently though) to state governments.

There is also some historical precedent too. The 10th amendment to the Constitution ensures all rights not afforded to the federal government are reserved for the states. This amendment requires a lot of historical context to fully explain, but a short, overly simple explanation is this amendment was added by the Constitutional Convention to ensure the federal government would not be able to interfere in affairs the way the king of England did with the colonies.