My 2cents explanation:
Sleep saves your current Windows session to RAM - Random Access Memory.
Power MUST be maintained or the Windows session will be "Lost" and you get an error message when restarting the PC.
Hibernate saves your current Windows session to a Hard Drive (HD) file (hiberfil.sys).
Power DOES NOT have be maintained to restore the Windows session.
HYBRID sleep does both a "save to RAM" (Sleep) and a "save to HD" (Hibernate) when the PC Sleeps, so the Windows session can be restored from either sleep or hibernate.
If the power does NOT go out while the PC is sleeping, it will wake up from sleep.
If the power does go out while the PC is sleeping, it will resume from hibernate (slower).
Think of Hybrid as adding an insurance policy that the PC will work correctly when waking up, even if the power did go out during sleep.
I use HYBRID sleep and I can pull the plug out of the wall when the PC is sleeping.
I use Desktop PCs.
If you have a LAPTOP, hibernate might be a better choice ...
Here is a tutorial by Brink with a more technical/detailed explanation of Power States.
http://www.sevenforums.com/tutorials/153968-sleep-states-see-available-sleep-states.html