A city council, or such similar governing body of a city, controls local city taxes and decies city laws responsible for keeping the peace. They also are responsible for the upkeep of city property and infrastructure, like sewers or roads.
A good council member will be well-connected to their city, and have an advanced understanding of its current political climate and fiscal needs. They also must be good at working with people, and making compromises with other members, if need be.
Every Council member gets to discuss the current issues of their city, and discuss solutions for them. It is important to have someone on the council that can have a meaningful contribution to that discussion, so that the best solution can be found.