Ars Technica has an interesting article on the information paradox.
Simply put, any quantum-mechanical system contains what is called zero-point energy or vacuum energy, which is the lowest energy that the system can have. The effects of this has been verified experimentally through the Casimir effect, which is the result of resonant fields created by virtual particles, which are cancelling each other out in vacuum all the time.
Now, consider a black hole, with an immense gravitational field. In the vacuum near the event horizon, these virtual particles keep getting created and destroyed. Stephen Hawking proposed that every once in a while, a virtual particle will get pulled into the black hole. Therefore, the black hole effectively acquired negative energy and the other particle will escape the gravity of the black hole. Under other circumstances, this particle would be a virtual particle, however the act of the black hole acquiring the negative energy will make it a “real” particle, resulting in its emission. This emission is what is now termed Hawking radiation.
Comparing this with the thermal black-body radiation, it has been found that unlike thermal black body radiation, Hawking radiation contains no useful information about the source of the radiation. What this translates to is that the result of the Hawking radiation is independent of the matter entering the black hole.
Enter quantum entanglement, which effectively states that two entangled quantum states have a correlation despite spatial separation. Now, imagine a pair of elements from an entangled system. If you pushed one into the black hole and left the other outside, the system is effectively destroyed, violating a very basic precept of quantum mechanics.
John Preskill won the famous bet against Hawking and Thorne when he challenged the destruction of this information.
Of course, Hawking radiation remains controversial and people have suggested alternatives to work around this paradox. One of the work-arounds suggests modifying the laws around Hawking radiation so that under certain conditions, quantum mechanical systems are non-unitary in nature (i.e. taking something away and putting it back does not change the sum-total of the system). Others have suggested that Hawking radiation is not purely thermal but rather thermal radiation after some quantum state corrections, while some others have put forward that the information is merely stored elsewhere, which can be calculated independently.
Either way, this is extreme interesting for some of us physics geeks! 