The black-hole information paradox is a behavior of black holes seemingly required by physics but which also breaks established physical laws: the disappearance of information that ought to be preserved. The information involved is the state of things, i.e., everything in the universe about an instant in its history that determines its future, which is presumed also to be reachable only through a single sequence of such states and no two histories-of-the-universe can possibly reach the same state. If something falls into a black hole, some of the state becomes unobservable but nothing says it no longer exists. But when Hawking radiation was deduced from quantum mechanics and black hole models, and it appeared that black holes grow smaller and dissolve given enough time, it would seem that the information surely no longer exists. The question of whether this is true has bothered theorists, with efforts to work out whether it is true or whether there is some way the information is returned to the rest of the universe. Resolving the paradox depends upon working out the consequences of both quantum theory and general relativity and how they interact, and could require new physics. Some claims have been made that current theory does include means to preserve the information.
The information involved in this issue effectively includes the location, mass, and velocity of every particle in the universe. For centuries, it has been imagined that if you could know all this (with some additional such state as the physics was worked out, such as electric charge), in principle, you could work out the future. It has also been observed that the basic physical laws, i.e., our model of how the universe runs, work just as well if time were going backward as forward: you can work out the past as well as the future, and the universe could just as easily run in reverse. For example, two weights in space holding a compressed spring between them will be pushed apart, each achieving some velocity. If the two happened to be moving at the same speed along the reversed trajectories, they would simultaneously arrive at the spring and push it together, according to Newton's laws. Quantum theories include additional state (quantum numbers, constituting more of this information), but despite the consequence of the theories that we cannot know precisely what is happening, they continue to have an analogous determinism and reversibility and the law remains that the totality of the state of the universe can be arrived at only through one sequence of such states, the word information indicating what is preserved. If black holes are an exception, then physical laws need to be worked out that make that exception possible.
Among the proposed solutions is black hole complementarity, which presumes a cloning of the information that would normally be impossible, allowing it in this case because the two sets are separated by the event horizon.