A county island is an unincorporated area within a county that is surrounded by incorporated areas. For some reason, when the surrounding area grew, the island area was not annexed by the surrounding cities.

County islands are mostly found in the Western States, like Arizona. Understandably, they can cause issues, since the county must provide services that the city usually provides like police, fire, and garbage collection.

Source: Wiki, but the term came from this article about a bank robbery in a county island.