In the United States, power isn't just held in Washington, D.C. Instead, it is shared between the federal (national) government and the individual state governments. This system is called "federalism."
The federal government handles issues that affect the entire country. These include things like coining money, declaring war, managing international trade, and regulating immigration.
Powers not specifically given to the federal government are reserved for the states (under the 10th Amendment). This includes things like managing schools, issuing driver's licenses, and running elections.
Some powers belong to both the federal and state governments. Both can collect taxes, build roads, and create lower courts.
While local governments (cities, towns, and counties) aren't mentioned in the Constitution, they derive their power from the state. They handle the most immediate day-to-day services like trash pickup, local police, and street lights.