Hyper-V is a new feature that is included in Windows 8. It allows you to run virtual guest operating systems on your Windows 8 machine. Windows 8 includes the same version as was available in Windows Server, so consumers now get a fully featured virtualization product for free in Windows 8! Perfect if you want to learn tweaking, or working IT.
Hibernation is a standby option built into Windows that allows you to shut down your system in the exact state it is now, and allowing you to disable all power, eject your battery and still continueing where you left of when you hibernated your system.