U.S. federalism divides and shares powers between the federal government and the states. Each state has all powers not explicitly delegated to the federal government or reserved to the people.
Because of this arrangement, the states play vital roles in our lives: elections, state courts, policing, immigration, business regulation, environmental regulation, education, healthcare, roads, land-use policies (zoning), and even creating local governments!
Image: U.S. map from 1818, W&D Lizars.