Hibernate takes a snapshot of everything in RAM (including any running applications) and saves it to the hard disk in the file c:\hiberfil.sys, then shuts the computer down. When the computer is restarted from hibernation it boots a bit faster than a normal power up from scratch. Hibernation does not consume any power while the computer is off.
Use: When the computer isn't going to be used for an extended period, say several hours or more, like over night.
Sleep basically shuts down the computer except for some components like RAM, so the next time it is resumed, it will start very quickly. Note: sleep consumes a small amount of battery power.
Use: When the computer will be left for a short time, like at lunchtime or driving to or from work.