What quantum effect causes black holes to evaporate?

Hawking radiation is the quantum effect that causes black holes to evaporate. Stephen Hawking predicted it in 1974 by applying quantum field theory to spacetime containing an event horizon.

Quantum fields cannot remain perfectly still, even in what appears to be empty space. Near a black-hole horizon, the behavior of these fields means that a distant observer detects thermal, blackbody-like radiation. The popular picture of particle–antiparticle pairs forming at the horizon is useful as an illustration, but the full derivation comes from quantum field theory in curved spacetime rather than from particles simply escaping from inside the horizon.

The emitted radiation carries away energy, so the black hole loses mass. As it shrinks, its temperature rises because Hawking temperature is inversely proportional to mass. This creates a runaway final stage, although a complete description of the endpoint requires a theory of quantum gravity.

Hawking radiation is not the same as pair production in general, the Penrose process, or the Unruh effect. It is also extraordinarily weak for ordinary astrophysical black holes. A black hole with the mass of the Sun would take roughly 10⁶⁷ years to evaporate, vastly longer than the universe's current age.