County divisions, as the name implies, are used by the United States Census to collect statistics at a level below that of a county for the 50 US States, the District of Columbia, and several outlying territories.

The type of entity varies from state to state:

• Minor Civil Divisions are administrative units set up by 28 states below the county level, and used as county divisions by the Census.
  Please note that although some of these units exist in states other than the ones listed in parentheses, they are not used for the Census as county divisions (some are used at different levels of geography).
• Functioning Minor Civil Divisions have individual governments which provide services.
• Incorporated places often serve as MCD equivalents:
  
  • City (some cities in 20 states, which are parts of counties but not MCD's)
  • Pseudo MCD (Arlington County, Virginia)
  • Independent City (not part of any county -- Virginia, Maryland, Missouri, Nevada)
  • Borough (New York City, New Jersey, Pennsylvania)
  • Municipality(Northern Mariana Islands)
  • Village (New Jersey, South Dakota, and Wisconsin, some villages in Ohio)
• Unincorporated minor civil divisons with functioning governments include:
  
  • Plantation (Maine)
  • Reservation (some "American Indian Reservations"¹ in Maine and New York)
  • Road District (Potter County, Pennsylvania)
  • Town refers to a unit in Connecticut, Maine, Massachussetts, New Hampshire, New Jersey, New York, Pennsylvania, Rhode Island, South Dakota, Vermont, or Wisconsin, none, some, or all which may be urbanized. It doesn't matter. The town = the local government.
  • Township refers to a similar unit in New Jersey, Pennsylvania, Michigan, Ohio, Indiana, Illinois, Wisconsin, Minnesota, North Dakota, Kansas, and Nebraska. In Missouri, some townships have governments, others do not.
• Nonfunctioning Minor Civil Divisions include:
  
  • Assessment District (Anne Arundel County, Maryland)
  • Barrio (Puerto Rico)
  • Barrio-Pueblo (Puerto Rico)
  • Beat (Mississippi, Alabama; now disused)
  • Census Subdistrict (Virgin Islands)
  • Election District (Guam and most of Maryland)
  • Election Precinct (Illinois and Nebraska)
  • Gore (Maine and Vermont)
  • Grant (Maine and Vermont)
  • Island (American Samoa)
  • Location (New Hampshire)
  • Magisterial District (Virginia, West Virginia)
  • Municipal District (Guam)
  • Parish governing authority district (Louisiana)
  • Police Jury ward (Louisiana, now disused)
  • Precinct (Illinois, Nebraska)
  • Pueblo (Puerto Rico, now disused)
  • Purchase (New Hampshire)
  • State (Palau)
  • Township (Arkansas, New Hampshire, North Carolina, part of Missouri)
• Unorganized territory refers to an area in one of nine states (Arkansas, Iowa, Kansas, Louisiana, Maine, Minnesota, North Carolina, North Dakota, and South Dakota) that is not included in any legally established minor civil division.
• Census County Division is a unit used in twenty-one states (Alabama, Arizona, California, Colorado, Delaware, Florida, Georgia, Hawaii, Idaho, Kentucky, Montana, Nevada, New Mexico, Oklahoma, Oregon, South Carolina, Tennessee, Texas, Utah, Washington, and Wyoming) where MCD's have not been set up, or (e.g. Delaware Hundreds) are unreliable for collecting statistics (i.e. they change a lot).
• Census Subarea is a unit used in Alaska.

The source for most of this writeup was the Glossary of geographic terms for the US Census. It listed these terms alphabetically and didn't always say where they were used. That took a bit of research.

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¹Yes, this is an official term of the US Census.