Like many people have said here, he's probably talking about unitarity. Susskind is echoing the general view among physicists. I don't think we have (yet) a concrete way to even precisely formulate the principle, leave alone any kind of proof. But based on unitarity in quantum mechanics and (for what it's worth) physical intuition about gravity, it seems like the sensible thing would be for information content to be conserved.
A simple illustration of this principle would be the no-cloning theorem. The way I see it, it says that you can't destroy the information in the register (the qubit into which you cant to copy some information) in a way consistent with unitary evolution. If you managed to do it, then you should be able to invert the unitary evolution and generate the information from the register which you're supposed to have destroyed.
As for hidden information, think of it as being temporarily hidden. When some information is inside the black hole, you can't access that information and the black hole has a corresponding entropy. When the black hole evaporates away, there is nothing left to contain the entropy, so the information must have been sent out somehow and it's now un-hidden (or so it's believed, as of today). Again, I don't think there's a concrete calculation to establish this definitively -- mainly since we don't have a good handle on quantum gravity.