Auxiliary(AUX) Inputs are tracks that pass audio through them without the need for the audio passing through to be recorded. They can be used as returns, sub mixers and bus masters.
An example of aux track use would be a drum sub mix, where you would bus the outputs of your drum tracks to a stereo aux track and control the overall volume of the drum kit with the stereo aux.
Another example of aux track use would be when using external synthesizers and/or sound modules with Pro Tools. The outputs of the synthesizers can be routed to and through aux tracks, and since you are controlling them with MIDI, and bounces contain any audio passing through the default outputs, there is no real need to necessarily record them to audio tracks.
There are many different uses for aux tracks.