It's when everything isn't moving around the 0 mark, if you played it though a hard core hi-fi purest amp the speaker cones would be instantly pushed in or out a bit and it'd vibrate around that point rather than around their natural point of rest.

usually obvious in audio files as the wave form is shifted up or down a bit ... most software has a remove dc offset function. to be honest unless you are recording something messed up you shouldn't see a dc offset very often although you can create them with some messed up plugin's and they are best removed.

in reality you get decreased headroom from having stuff with offsets in ... dunno if it affects quality much more than that although it'd be a shocker to see it on a mastered cd.