A precinct is any one of the sections that a town or city is divided into when people vote in an election.
Please note: The term "precinct" has several different uses. It can, for example, refer to a division of a police department in a large city.
U.S. Census Bureau
Instead of using the term "precinct," the U.S. Census Bureau uses the term "voting districts." Voting districts (VTDs) refer to the generic name for geographic entities, such as precincts, wards and election districts, established by state governments for the purpose of conducting elections.