Final answer:
County governments administer state laws, handle judicial and tax matters within their regions, and vary in size, with the largest county over 88,000 sq mi and the smallest above 2 sq mi. There are over three thousand counties in the U.S., each run by elected Supervisors or Commissioners.
Step-by-step explanation:
County governments serve a larger geographical area than cities and towns, but a smaller area than states, operating under provisions set out in the state constitution. They have a variety of duties, such as keeping the peace, maintaining jails, collecting taxes, and much more. According to Brian Lavin's 2012 Census estimates, there are just over three thousand counties in the United States.
The size of counties can vary greatly, with the largest county measuring more than 88,000 square miles. In comparison, the smallest county measures more than 2 square miles. County systems can take one of three basic forms: the commission system, the council-administrator system, and the council-elected executive system. Counties are led by elected officials often referred to as Supervisors or Commissioners.
Historically, during the era of territorial expansion, the territory of an empire would be divided into commanderies and counties. Each county was headed by a centrally-appointed magistrate responsible for a range of administrative and legal duties, further emphasizing the administrative importance of the county structure.