Auxiliary sends on mixing consoles have two main functions…
1) Foldback for musicians (headphones in the studio or wedge monitors on stage).
In this case, you will make a headphone mix that has to be completely independent of the recording or FOH (Front of House) mix. Otherwise the musicians will hear what you are doing to please the recorder or audience. Musicians HATE their foldback levels going up and down, which to them will seemingly be at random.
Therefore you should use a PRE-FADE auxiliary send that is not affected by the position of the fader.
2) To add reverb. Reverb is an effect where the processed signal is mixed in with the original signal.
In this case, suppose you faded out the dry signal. You would want the reverb signal to fade out too. In fact, whatever reverb level you set, you want it to be in proportion to the level of the dry signal.
Therefore you use a POST-FADE auxiliary send where the amount of signal sent through the aux is proportional to the fader position.