The city council is the legislative branch of a local government. It passes laws and ordinances (sometimes with the help of a mayor who has veto power). In some cities, elected city council members run as partisans — they represent a specific political party and their votes are counted accordingly when election time comes around.
Aside from passing legislation, city councils have many other powers that affect our daily lives. For example, they can pass zoning laws that dictate what can get built where (e.g., can you turn that old factory into apartments?) and can set rates for things like trash collection and utility bills. They can also set city policy and appoint people to various city boards and commissions, including school board members and community advocates.
Most of the important work of your city council happens outside of city council meetings, in committee hearings and other discussions. These are where council members debate proposed laws, hear updates from agency representatives and from New Yorkers like you who attend to share their thoughts and concerns. Every council member is assigned to a committee through a vote by their colleagues and they sit on panels that focus on issues such as housing, transportation, infrastructure and more.
At the start of a meeting, the council chairperson takes a roll call and officially opens the meeting by calling the assembly to order. Then the agenda gets passed across the room, listing everything that will be discussed or acted upon. By law, the agenda has to be published in advance of the meeting.