You should choose this mode if you don't know how long you won't use your computer but want to have the same desktop state when you resume

Solution(By Examveda Team)

This option was designed for laptops and might not be available for all PCs. (For example, PCs with InstantGo don't have the hibernate option.) Hibernate uses less power than sleep and when you start up the PC again, you’re back to where you left off (though not as fast as sleep).

Use hibernation when you know that you won't use your laptop or tablet for an extended period and won't have an opportunity to charge the battery during that time. First check to see if this option is available on your PC and if it is, turn it on.

Source : microsoft.com