From the Wikipedia page 
Political divisions (also referred to as administrative divisions) of the United States are the various recognized governing entities that together form the United States. The first-level political (administrative) division of the United States is the state. There are 50 states, which are bound together in a union with each other. Each state holds governmental jurisdiction over a defined geographic territory, and shares its sovereignty with the United States federal government. According to numerous decisions of the United States Supreme Court, the 50 individual states and the United States as a whole are each sovereign jurisdictions.
All state governments are modeled after the federal government and consist of three branches (although the three-branch structure is not Constitutionally required): executive, legislative, and judicial. They retain plenary power to make laws covering anything not preempted by the U.S. Constitution, federal statutes, or treaties ratified by the U.S. Senate, and are organized as presidential systems where the governor is both head of government and head of state (even though this too is not required). The various states are then typically subdivided into counties. Louisiana uses the term parish and Alaska uses the term borough for what the Census terms county-equivalents in those states.
Counties and county equivalents may be further subdivided into townships. Towns in New York, Wisconsin and New England are treated as equivalents to townships by the United States Census Bureau. Towns or townships are used as subdivisions of a county in 20 states, mostly in the Northeast and Midwest.
Population centers may be organized into incorporated cities, towns, villages, and other types of municipalities. Municipalities are typically subordinate to a county government, with some exceptions. Certain cities, for example, have consolidated with their county government as consolidated city-counties. In Virginia, cities are completely independent from the county in which they would otherwise be a part. In some states, particularly in New England, towns form the primary unit of local government below the state level, in some cases eliminating the need for county government entirely.
The government of each of the five permanently inhabited U.S. territories is also modeled and organized after the federal government. Each is further subdivided into municipalities. Guam uses the term Village and the U.S. Virgin Islands uses the term Districts, American Samoa uses the terms district and Unorganized atolls.
Other U.S. subnational divisions include the District of Columbia, several minor outlying islands, and Indian reservations, all of which are administered by the Federal government. Each Indian Reservation is subdivided in various ways. For example, the Navajo Nation is subdivided into agencies and Chapter houses. While the Blackfeet Nation is subdivided into Communities. The Federal government also maintains exclusive jurisdiction over military installations and American embassies and consulates located in foreign countries. Other special purpose divisions exist separately from those for general governance, examples of which include conservation districts and Congressional districts.