Ah! It means to pay attention, basically. It comes from an old saying about typing on a typewriter, I think! Something about being careful about what buttons you are pressing?

The theory I've heard is that it refers to "please" (P's) and "thank you" ([than]Q). Whether it's the real origin or not, I don't know, but it does fit the meaning of the idiom well.

This is one of those idioms that causes a lot of arguments among native speakers especially its origins Basically it means mind your manners and be polite. There are several theories about where it came from.

There doesn't seem to be a definitive answer on this. One suggestion is that it refers to reminding children to be careful when learning to write as lower case 'p' and 'q' are the same, just reversed. The expression goes back well before typewriters, and anyway, the p and q on a keyboard are about as far away from each other as it is possible to be so any connection to that seems most unlikely.

Oh wow, this expressions even has its own Wikipedia page: http://en.wikipedia.org/wiki/Mind_your_Ps_and_Qs