A mayor is a person who is in charge of the administration of a city. Some mayors are elected by the people who live in that city. For other cities, a central government body may choose the mayor. Some large cities have a Lord Mayor.
In federal countries like Germany the mayor can also be head of the government of a city state. The Mayor of Hamburg runs the government just like the Minister President of Bavaria runs the Bavarian government. In some big cities such as Tokyo the Mayor is a Governor.
In many countries, such as the United Kingdom and Australia, the mayor is not in charge of the daily functions of a city or town. That job is done by a Town Clerk or Chief Executive, who is appointed to a full-time paid job. The mayor works part-time, usually without payment, and represents the city at events and civic functions.