Hawking radiation (a phenomenon first theorised by Professor Stephen Hawking in a 1975 paper entitled ‘Particle Creation by Black Holes’ ) is what happens when virtual particles form near the horizon of a black hole. The Hawking radiation is not actual radiation but it effectively behaves in a similar way to black body radiation.
A virtual particle is a temporary violation of the conservation of energy law, in that a particle is created “from nothing.” This is caused by zero-point energy fluctuations in the quantum foam. However because the particle exists for too short a time to be measured, it gets away with it as far as physics is concerned. The virtual particle is in reality an entangled system of a particle-antiparticle pair, which annihilate each other almost instantaneously.
These ‘quantum jitters’ as they are sometimes called, snatch gravitational energy away from the black hole in order to occur. Despite there being only a tiny distance between the pair, the black hole’s gravitational forces have a remarkably steep gradient, and the two particles may feel drastically different tidal forces acting on them. One of them may escape, but the other may not. Upon escaping the black hole’s clutches, a free particle will become realised through ‘measurement’ as it interacts with the universe around it. Because of this, the virtual gravitational energy it stole also becomes real. The black hole’s gravitational energy loss converts to the loss of a small amount of its effective mass. Yes it does absorb one of the particles (which also becomes ‘real’ through entanglement with its twin), but it paid for two.
A lonely black hole, starved of food, will eventually evaporate away in this manner. Thus the energy conservation law is not violated after all.