I don’t know about other states, but in upstate New York a village is a legal entity that is a defined area within a town. A town is a subdivision of a county.

In other states, I think they don’t fully subdivide counties. So every person in one of those states either lives in an unincorporated part of a county, or a town/city. Those who live unincorporated are only governed by the county, while those in towns/cities are governed by both town and county.

So in New York there are no unincorporated parts of counties. Everyone lives in a town, which is part of a county. Some people may also live in villages, which are areas in towns.

Edit: for example, the village of Seneca Falls is in the town of Seneca Falls, which is in the county of Romulus.