Hawking radiation is the way in which black holes evaporate. It is named for Stephen Hawking, the first person to perform the calculations demonstrating that it is possible.
There are several ways to formulate Hawking radiation. This comes from the multiple ways in which quantum laws can be formulated. The simplest description is based on particles rather than waves. (All descriptions must deal with the particle/wave duality at the quantum level.)
Vacuum fluctuations are subject to the laws of particle/wave duality. The waves fluctuate randomly leaving positive energy in one place and negative energy in another with zero average energy. The particle aspect is related to the separation of positive and negative energy. In regions where there is positive energy, a virtual particle (they always appear in pairs, matter and antimatter) can be produced. These virtual particles borrow energy from the neighboring regions. Under normal circumstances the two particles then annihilate each other and disappear, giving their energy back to the neighboring regions.
When this happens near a black hole sometimes the following can happen. The virtual particles can easily separate from each other so long as they remain in the region where the electromagnetic field has momentarily acquired positive charge. This is normally about the same as the wavelength of the fluctuating electromagnetic wave. If the wavelength is long enough the virtual particles (usually photons) can easily travel far enough apart for the tidal effects of the black hole to pull on one particle with a huge force.
This tidal force feeds energy into the particles to convert them into real photons and have sufficient energy left to return to the neighboring, negative energy regions of space. The photons, now real, are in two different locations. One is inside the horizon of the black hole and is lost. The other is outside the horizon and has escaped the black hole forever. The particle that has escaped the black hole is carrying with it the energy that the black hole "donated" to its creation. Because energy and mass are interconvertable by E = mc2, the mass of the black hole has been reduced by the mass of the photon that was created.
