Hawkings theory is basically this:
Matter is constantly being created and destroyed in "empty" space. A positron pops into existence coupled with its antimatter counterpart, and they quickly annihilate each other (we're talking sub-nano seconds here). But, what happens if the antimatter particle falls into a black hole before it can match up again with its counterpart? Effectively, a positron is just left out there, thereby creating matter. However, this can only happen around the fringes of a black hole.