Federalism is defined as "A system of government in which power is divided between a central authority and constituent political units". This means that the US government is divided into separate groups from federal to state levels.
This image shows how the federal government has power and contact over all below it. Then comes the state, to county, to city, to the family. This allows for less work for each of the groups above it. They no longer have to worry about all the other parts, just a selected portion. Most governments in the US are run using a Federalism structure, but may be called by different names.