Hibernate (to put is as simply as possible) is a state of the computer/laptop when the whole data in RAM is dumped to HD and then powered off COMPLETELY.
Compared to Sleep, where nothing is really saved, just enough power is used to keep the RAM powered and other components either turned off or kept up using minimal power. If you were to lose power/shutdown by accident in while in Sleep mode, you'd lose everything you were doing.
Hibernation takes more time to come back up from its state compared to sleep, but is better on battery.