As far as I know, Hawking Radiation has been attributed to Vacuum Fluctuation (read Despot's writeup) in which 2 particles are created spontaneously when quantum fluctations allow. These particles are of opposite charge and normally are attracted back to each other and the annihilate themselves.
When this happens at the event horizon of a black hole (or further out, depending on the velocity of the particles), 1 particle will be pulled into the black hole and the other will escape. Since the energy (and therefore the mass) to create these particles comes from the black hole and only half of it returns, the black hole itself has lost mass.

In reality, the mass of other outside particles pulled into the black hole is so great that most people wouldn't even notice the difference that Hawking Radiation makes on normal black holes. It only becomes apparent when it is smaller and therefore swallows less mass.
See What if a black hole was created on earth?