Sleep, sometimes also called suspend, is a state where the computer is set in a low power consumption state, turns off screen and hard disks and just uses enough energy to keep the RAM alive and watch for certain events for waking up, but really it doesn't do any processing in the meantime. When you return to work, it restores its previous state from RAM and resumes operations, but if it's for some reason powered off or unplugged, all the work is lost and must do a fresh restart.
In hibernation, the computer is totally powered off, but prior all RAM contents are dumped in a system file, from where it can latter can be fully restored to its previous state. That way, you can even unplug, disassembly if you want, and when it's powered on, it will not do a normal bootup, but instead will read its working state from disk and resume where it was.
While both are similar, sleep is more suited for short interruptions of work, when power off would take too much time to justify, but you want a quick resume latter. Hibernation is better when you leave at night for example, the next day when you come back Windows will be in the exact same state as when you left, and with a faster boot time.