Hawking radiation postulates the permanent creation of particle-antiparticle pairs from a vacuum under the action of tidal forces in the neighbourhood of a black hole horizon as a result of quantum field theory. Generally, these particle-antiparticle pairs annihilate each other as soon as they form, unless some physical phenomenon succeeds in separating them in less than their lifetime.
This can happen at the horizon of a black hole, a place where the gravitational tidal forces are so strong that they can separate the two components of the pair, one of them being absorbed and the other escaping.
In practice, Hawking radiation turns out to be extremely weak for black holes on a stellar or supermassive scale, and it cannot currently be detected. But it could become observable for microscopic black holes such as must have formed in the Big Bang, called primordial black holes, of which the creation in particle accelerators is envisaged.