Heisenberg's principle allows you to temporarily violate energy conservation laws (e.g. create pairs of particles out of nothing) as long as you repay everything in time. The larger the particle-antiparticle pair, the quicker it has to be repaid. Converting a virtual pair to a real pair without repaying the debt can be seen as generating a bit of negative-energy "exotic matter" (whatever that is) to represent the unpaid debt. Its energy is equal in size to the pair with the opposite sign. This then falls into the black hole along with one of the particles, decreasing the mass of the black hole overall.
The horizon of the black hole gets in the way of recombining some virtual pairs, so these conversions virtual->real will happen.
I found this lecture with the same idea (more detailed and less butchered): http://teacher.pas.rochester.edu/Ast102/LectureNotes/Lecture19/Lecture19.pdf