What is the function of a generator?

There are several different types of generators. I'll explain how a "large" 3 phase synchronous generator works - the type that most likely is generating the power you're using at work or home.

The generator is only a small part of a power plant. It is composed of two sets of windings, one on the stator, or stationary part of the generator, and the other mounted on the rotor, or rotating part of the generator. Usually the rotor windings have voltage applied to them by an outside source that is controllable by the power plant operators through what is called the "voltage regulator".

A power source is used to spin the rotor. This can be a steam turbine, a wind turbine, and many others. As the rotor spins, it induces current in the stator windings in proportion to the amount of power applied to the rotor windings by the voltage regulator (VR). This current flows out of the stator windings, which are connected to a load through the transmission system. This current, in turn, induces a reverse force (called "back emf") on the rotor winding. The back emf causes the rotor to slow down. As the rotor slows down, the governor (a system that monitors the generator's speed, and keeps it within a certain range) kicks in to speed the generator back up.