A black hole is characterized by two elements: the central singularity, a point where space-time stops making sense; and a horizon of events, which surrounds the singularity. It is called this because it represents the horizon beyond which a phenomenon can be observed: an astronaut outside this limit could never see what happens to a colleague who would end up on the other side. And this is because, within the horizon of events, gravity is such that not even light can come out of it.
However, the astronaut who falls into it could experience a particular phenomenon if not immediately destroyed by the tidal forces. Falling gradually towards the singularity, space-time would expand to infinite values. The unfortunate astronaut would see in a few moments the future history of the whole cosmos, until his last lament.