What are the duties of an ATC supervisor?
In the FAA, there are two types of &quot;supervisors&quot; who might be on duty at any given time: a genuine managerial supervisor, who is part of the managerial pay scale and is not part of the bargaining unit (union); or a &quot;controller-in-charge,&quot; a &quot;line&quot; controller (a bargaining unit employee) who has been certified to perform most but not all supervisory duties if a supervisor is on break, not scheduled that day, etc. Sometimes the supervisor or CIC will be working a control position, or they might be working at a desk in the back of the operation not talking to any aircraft directly.
In either case, the general duties of the supervisory position are:

Running the shift (determining the break schedule, approving sick leave, etc)
Assigning controllers to combine or decombine control positions as traffic and complexity warrant
Assigning on-the-job training to ensure trainee controllers get sufficient training time
Monitoring the operation and, if they feel it is necessary, instructing a controller to take a specific action to ensure safety (this happens very rarely!)
Coordinating with surrounding facilities—not about individual aircraft (the controller on position does that) but about traffic management initiatives, contingency situations (e.g. telling people &quot;we lost commercial power so we're on generators, be prepared in case we lose those too&quot;), etc
Answering the commercial phone if people call (survey pilots informing where they will be operating, military ops calling to see if a plane can come do practice approaches, someone claiming they saw a UFO, noise complaints, etc, etc)
Keeping the daily log up to date (logging equipment outages, runway closures, etc)
Coordinating with other facilities or airport operations regarding emergency aircraft or crashes

The CIC authorized to carry &quot;on the spot&quot; corrections—telling the controller on position they need to do something else for safety reasons—but is not authorized to perform personnel actions like officially counseling a controller about a loss of separation. That's reserved for the actual supervisors.
Of note, if you hear a controller give an instruction and then another controller comes on the frequency and gives a different instruction, that isn't a supervisor. That's the instructor plugged in alongside their trainee controller. During training the certified trainer controller is responsible for the position, so they will give their trainee latitude to make their own mistakes but will step in to prevent an actual safety event.