An Audio Engineer is a person who in some way engineers the audio for a particular purpose. In the real world however the definition is usually narrowed down to the people doing the mixing (so no, the guy setting up mic stands doesn't count, they have their own titles). The most common places they are found in are usually:

recording studio
concert halls, stadiums, and other music venues

The primary job of an Audio Engineer (by which I mean the person mixing the show) is to make sure that the sound is reproduced accurately, and if possible, better than the original. This is not such an easy task. Depending on the complexity of the system it can take quite a bit of work to prep and operate a system.

Lastly, as a tech, don't come up to the tech during intermission and talk to them about the sound system or other such things, chances are they have 30 million other things to do, and the last thing they want to deal with is getting past an annoying patron.