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In the past, villages were where most people lived. After the Industrial Revolution, when people started making a lot of things in factories, people lived more in towns. Moving to towns is called urbanization.
In twenty US states, a "village" is a sort of local government, similar to a city but with less power and for a smaller place. But this is not so in all the United States. In many states, there are villages which are bigger than the smallest cities in the state. The difference is not the population, it is how much power the different sorts of places have, and what they do for people living there.
New York state
In New York state, a village is a place which is usually called a town.
In many states, a "village" is only a place where people live, with no legal power, similar to a hamlet in New York state. The name for these is "unincorporated villages".