Big impacts the ground up.
Have you ever received a speeding ticket? If so, then you've dealt with your local government. The police officer was likely a city employee, and you probably appeared in or made a payment to the city court.
Local government is the public administration of towns, cities, counties and districts. Notice that this type of government includes both county and municipal government structures. It can be challenging, but these entities must work together to administrate a particular geographic area.
As citizens, we have much more contact with our local governments than we do with the federal government. This is because local government runs our city utilities, libraries, fire departments, public swimming pools, parks, local law enforcement and many other areas of our everyday lives.
The organization of local governments varies depending on the state. However, all local governments derive their authority from the state in which they are located.