Basically, Hawking's "information paradox" starts with the idea that the entire universe is made of information, and information can never be lost. That is, that no matter how much it is cut up, pulverized, scattered, whatever, the information never actually goes away (i.e., it never actually becomes nothing).
So, as I understand it, the Q.P. theory of information is that something can never become nothing. It may change into a form that looks like what we perceive as "nothing," but it's not actually nothing because information cannot be lost (i.e., it cannot completely go away).
Think about the mass of a log you burn: some of it becomes gas, particles in the air, ash that goes into the ground, etc. It stops being a "log," but it's mass just redistributed.
This theory of information led to the "information paradox." Hawking then found through quantum physics that, despite theoretical calculations demonstrating that information could not be lost, information did seem to go away, leave the universe, be lost. This created a great paradox (heresy!) that threatened the physicist's concept of what is "real."
Again, as I understand it, this led Hawking on a great quest to prove the theory of information either wrong or reconcile it with the apparent "loss" of information. This led to mathematical proofs that information --- remember this means the very essence of all physical and even "mental" matter (memories, for example) in the universe --- is not lost but changes form at the very edge of black holes and, he said, passes into a parallel universe.
So, according to this Q.P. proof, information is not "lost," it merely changes form and is retained in a separate but connected universe.
I'm sitting there watching two long documentaries on Hawking and this debate, and, to me, there was no escaping the similarity between what Hawking said quantum physics proved about the information paradox and what Christians believe about the status change we call "death" and how a person's "information" passes to a parallel universe (what Christians view as the spiritual or heavenly realm).
Hope that was neither too jargon-y nor too simplistic. Just throwing it out there for starters. Again, I am not a physicist, so can't debate the fine points of Hawking's calculations. Thanks for asking.
A related article: Quantum Physics and "Them Dry Bones."
And thx for the Hawking link!