Hibernate takes a snapshot of everything you got on RAM (including any windows and apps running) and saves it to a special hard disk file and then shuts the computer down, when you resume from hibernation the computer boots a bit faster than a normal power up bootup. This method does not consume any power while the computer is off.
Uses: When you are not going to use the computer for a few hours or more.
Sleep, basically shuts your computer down except some components like RAM, so the next time you resume, it will boot almost in an instant. However, this method consumes battery power.
Uses: When you are just leaving the computer for a few minutes or hours, like at lunchtime or something like that.