Sleep puts the computer in a low-power mode. The CPU and hard drives are turned off, and only the RAM receives power. Upon some form of input, the computer powers back up to where you left off.
Hibernation stores all the contents of RAM to the hard drive and powers off completely. When the computer is powered back on, the kernel loads the saved contents back into RAM.
Thus, Sleep is faster to respond back to life, and hibernation allows you to shut the computer down and even unplug it.