Stands for Pretty Damn Quick. Usually used in a slightly hostile sense. Ex:

Boss: You better get that project done PDQ or you're canned!
Peon: Yessir.

I personally hardly ever use this abbreviation. I think that you should try and live a life where nothing ever has to get done PDQ. PDQ just leads to stress and anxiety. I doubt you will ever hear me demand something PDQ, except maybe from myself(ie I better get this paper done PDQ, or I'm gonna fail that course). I also don't like it when people demand things from me PDQ. If it's that important, DIY.