There will be different ways to describe various roles played by a supervisor and there will be differing opinions (from text to text) as to which of these functions are "major." The link below, for example, lists no fewer than 12 roles that a supervisor must play.
At the most fundamental level, though, the role of a supervisor is to make sure that the work of the factory gets done in a timely manner and that the quality of work done is as good as it can be.
In order to do this, the supervisor must function as an intermediary between the higher levels of management and the workers on the floor of the factory. In other words, another major function of the supervisor is to deal with both the white collar levels of the company (from whom the supervisor takes orders) and the blue collar workers (to whom the supervisor gives orders).
In this way, the two most basic functions of a supervisor are to act as an intermediary between management and labor so as to ensure that the manufacturing is done quickly and well.