(1) you are a US Citizen, (2) you are a legal adult, and (3) you are a permanent resident of the entity you wish to become mayor of (that is, you are a resident of the city/town/etc. where you are running for mayor).
It varies by juristiction. For most places in the United States, there are really only three requirements: (1) you are a US Citizen, (2) you are a legal adult, and (3) you are a permanent resident of...
A mayor is in charge of making many of the decisions in a city. He/she can help with recreation. Such as parks, libraries, post offices, etc. They also help with fire departments and police. The...