The words were Hawkings's, not mine. Possibly I cut off the quotation too soon, but the explanation went on for a couple of pages. To summarise as best I can:

In a normal situation particles and anti-particles are coming into being and destroying each other all the time. In the region just outside the event horizon it is possible for one of the particle/anti-particle pair to fall into the black hole across the event horizon (which would have to be a one-way trip) thus leaving the other particle floating about without anything to annihilate with. For reasons I didn't quite grasp, it is the anti-particle which tends to fall into the black hole leaving the particle to its own devices. The result is it looks as if the black hole is radiating particles, but that is not what is actually happening.

Bingley

Bingley