A municipality refers to a village, town, or city that's usually governed by a mayor and council. From this noun, we get the adjective municipal, which you can use to describe something that relates to a town or its government.
Your town's city council may have offices in the municipal building downtown. If you want to fight city hall, that would be the place to go. Municipal also more generally describes anything related to the town or city itself. If you live within the city limits, for example, your house may be hooked into the municipal water supply, but if you live outside the city limits you may have to have your own well.