To put it simply, hawking radiation is how black holes lose energy and eventually evaporate.

The event horizon is basically a distance from the center of a black hole at which anything that gets close will fall into the hole while anything that doesn't cross the line still has a chance to escape. The theory is that space itself is constantly in flux, with particle-antiparticle pairs constantly forming and immediately eradicating themselves everywhere. When one of these pairs forms at the event horizon, one of the particles is able to escape while the other falls into the black hole, chipping away at the matter therein. The escaping particle then carries some energy from the black hole out into space in the form of kinetic energy.