There are many types of managers. For example, a project manager's role is to track progress of a project, reveal and resolve deadlocks (A waits on B, B waits

There are many types of managers. For example, a project manager's role is to track progress of a project, reveal and resolve deadlocks (A waits on B, B waits on C, C waits on A), communicate progress to the outside and so on. In other cases, managers act as proxies for teams. If you want something from a team, nobody expects you to talk to all 12 members and convince everybody -- instead you talk to the manager, and the manager then talks to the (relevant parts of the) team. From the team's perspective, a good manager shields them from most of the company's politics, declines nonsense requests early on, organizes all materials necessary for the team to work etc. In general, managers are paid well because they carry a lot of responsibility. Even a brilliant team will underperform under a terrible manager, and a very good manager can bring out the best in teams.