Hibernation mode is for energy conservation. It's more useful if your using a battery to run your computer, like with a laptop. Your computer goes into hibernation mode after long periods of inactivity also if your battery runs too low it'll hibernate so you don't loose any data. See:
Power Management
If your connected via a power cord, like with a desktop. You can safely turn it off. I have mine shutoff and I've never had any problems.