Not strictly related to the screen saver (which protects the monitor from burn in), Hibernate is a power saving feature typically used by laptops running on battery power. If you don't use the PC for a set period of time, Hibernate kicks in and dumps an image of memory to disk then switches off. When you power back up the image is restored to memory and the PC is back exactly where you were ... unless it goes wrong in which case you get the BSOD!
To disable, look in Control Panel -> Power Options.
You can set "Hibernate" to "Never" under the relevant power schemes, but quickest just to uncheck the tick box in the "Hibernate" tab.
RC