Hibernation is when, instead of shutting down, the computer saves the contents of the RAM to the hard drive, and modifies the startup sequence when the computer next starts up - so instead of starting up normally, all it does is load the data back into the RAM and start off from where it was. Its supposedly quicker than a cold start.
This is different from sleep, which only suspends the PC - the data remains in the RAM and the PC continues to use power.
