I thought I’d write what I already understand about the role of a compositor:
A compositor’s role is to bring together the elements that might make up a shot. These elements might often be character animation, background layers, effects, etc.
In the case of a small studio, a compositor may be expected to grade the footage, but this would be a specific role in larger studios.
Bringing together the elements of a shot requires a good understanding of staging, composition and perspective. Even when a shot has been story-boarded and laid out, there may still be unexpected problems with how it all fits together that will need to be ironed out for the shot to make sense.
A compositor may have to work with the layout artist or even be the layout artist on smaller productions to put together backgrounds that work with the animation on screen.
A compositor may have to work with both 2D and 3D elements as, more often that not, even 2D animated films will have 3D assets in shot, for example the CG cars in ‘The Illusionist’.
The most common compositing softwares are After Effects and Nuke.