Quantum Unitarity
In quantum mechanics, the evolution of a closed system is unitary. This means information is never destroyed; the past uniquely determines the future, and vice versa. If you know the final state, you can theoretically reconstruct the initial state.
The Problem with Hawking Radiation
Hawking radiation is purely thermal. It depends only on the mass, charge, and angular momentum of the black hole, not on the specific details of the matter that fell in. When the black hole evaporates completely, the thermal radiation remains, but the detailed information about the initial matter seems to vanish.
The Information Paradox
If information is truly lost, quantum mechanics is incomplete or incorrect. If information is preserved, our understanding of spacetime and horizons must be revised. This is the Black Hole Information Paradox.