Finding the city or town you are in
The page reads your position and asks OpenStreetMap which city, town or village contains it. The name appears in large type on the green sign, like the destination on a highway guide sign, with the county and state underneath.
People ask this on road trips, when a navigation app has stopped naming towns, when they have woken up on a train or bus, after moving to a new area where towns run into each other, or when a delivery form or a local service wants to know which city they are in.
City limits versus the name on your mail
There are two different answers to "what city am I in", and they often disagree. One is the municipality whose boundaries you are inside, which decides who collects your taxes, runs your police and sets local rules. The other is the city name in your mailing address, which the post office chooses based on which post office delivers your mail.
This page reports the first one where the boundary is mapped. So a house outside any city limit might show the nearest village or no city at all, while its mail says a larger city nearby. Neither is a mistake. See why your address says a different city for more on how this happens.
What you see if you are not in any city
Much of the United States, by land area, is unincorporated. There is no city government, and services come from the county. If you are in one of those areas, the sign shows the nearest named place the map has for you, which might be a small community or a hamlet, or it falls back to the county name.
The name of a community that is not a legal city is still useful. It is often what locals call the place and what appears on road signs, even though the area has no city hall.
Other countries work differently. Outside the US the sign shows whatever the local map calls your town or municipality, and the second line shows the county or district and the region.
Towns, villages, townships and boroughs
US states use different names for their local governments, and the tool shows whichever one applies. A town in New England is a different kind of government from a town in the Midwest. Many states have villages, some have boroughs, and many Midwestern and Northeastern states have townships, which are divisions of a county that may or may not provide services.
When the map records a city, the sign shows the city. When it records only a town, village or hamlet, it shows that. For formal purposes, your county's website is the reliable place to check which local government covers your address.