What does it mean if a town has a mayor-council system?

The mayor–council government system is a system of organization of local government. 

Characterized by having a mayor who is elected by the voters, the mayor–council variant may be broken down into two main variations depending on the relationship between the legislative and executive branches, becoming a weak-mayor or a strong-mayor variation based upon the powers of the office. 

The mayor-council system is a common form of municipal government in the United States. In this system a mayor heads a locally elected council. The mayor may be either popularly elected or elected by the council from among its members. There are two types of mayor-council government.