So, first off, we know that energy and matter are the same thing (E=mc2). So, when a particle-antiparticle pair gets created, they take some of the energy from local space. When they collide and destroy each other, they give back the energy they took.

At the event horizon of a black hole, energy (and therefore mass) gets taken from the black hole to create a particle-antiparticle pair. One of the particles gets freed into space and, thus, the black hole doesn't get back the energy that got taken from it. This causes it to be less massive. (It gets back half the energy that it gave to create the particle-antipartcle pair in the form of the single particle that it consumes)

So, when matter gets sucked into a black hole, it gets converted into energy. When Hawking radiation occurs, the energy gets transformed into matter again and gets spat out. Make sense?