Virtual particle pair production is constantly occurring in the vacuum because of the uncertainty of energy and time due the HUP. These virtual particles almost immediately annihilate because the time the particles are allowed to exist is inversely proportional to their mass energy.

however in the vicinity of the event horizon of a BH the tidal gravitation is so great that it forces the particles apart with such violence that enough energy is imparted to turn the virtual particles into real particles. At this point it is possible (actually required but I don't want to get into this) for one particle to escape to infinity and the other particle to be captured by the hole. So, in effect, what has happened is that the hole has expended enough energy to create two particles but only gets the energy of one particle back. In effect radiating energy. It is actually much more complicated than this but this will serve as a first approximation.