Hibernation is very similar to sleep (aka standby). Both will restore your windows session as it was before you put your computer to sleep.
Hibernation means your computer copies whatever is currently in it's memory to the hard disk, and shuts the machine down. Your computer will use no power while hibernating, but will take longer to boot up than if you had put it in sleep mode (but the boot will still be faster than if you had shut it down!). You will also lose a portion of your hard disk (equal to the amount of RAM you have) that Windows will reserve.
Sleep (or standby) means your computer leaves whatever is currently in your memory just where it is, and powers down the rest of the system, leaving a small circuit closed to keep your RAM powered. Thus, sleep uses your battery while sleeping! It will have the fastest startup time versus a cold boot or hibernate, and will not use any of your disk space.