A black hole forms where gravity is so strong that the escape velocity exceeds the speed of light, so not even light can leave. Because nothing travels faster than light, anything crossing this threshold is trapped.
The event horizon is the surface marking the point of no return around a black hole: outside it escape is still possible, inside it is not. An observer crossing it would notice nothing locally special, yet they could never signal back out.
The total area of a black hole's event horizon never decreases over time; when two black holes merge, the combined horizon area is at least the sum of the originals. This gives the horizon a quantity that behaves like entropy, always growing.
Contrary to being perfectly black, quantum effects near the horizon make black holes emit thermal radiation at a temperature inversely related to their mass. This means they lose energy, shrink over immense timescales, and can eventually evaporate entirely.
If a black hole evaporates completely into featureless thermal radiation, the detailed information about everything that fell in appears to be erased, which quantum mechanics forbids. The paradox is the clash between gravity seeming to destroy information and physics requiring it to be preserved.
Hawking proposes that information about what falls into a black hole is not lost but encoded in a disordered form on the event horizon, returning in the emitted radiation. The information comes back, but so scrambled that reading it meaningfully would be impractical.