The difference between hibernate and sleep or standby modes is mainly the amount of power saved and how the current data is being stored.

Sleep or standby mode saves your current work state (all open programs, etc.) in memory and cuts the power down to the bare minimum required to keep the memory in place, plus a few other crucial components. Since you're not fully shutting down, it'll restore your current work state as soon as you come out of Sleep mode. Also, since you're not completely shutting down, coming back out of sleep mode is alot faster than a full boot up or restart (or coming out of hibernation mode).

Hibernation mode also stores your current working state, but instead of saving it to RAM, it saves it in a file on your hard drive named hiberfil.sys, and then shuts completely down. When booting up again it reads the data from hiberfil.sys, restoring whatever your working state was when it went into hibernation, rather than booting up to a fresh desktop. Since nothing is running, there is practically no power being used, so it's the better option if you want to save maximum juice.