+1
Hibernate saves the current state of the PC to the hard disk so that all power can be turned off and it can be restarted where it was before from the hard disk.
Standby powers down all non essential parts of the lappy like hard disk, monitor etc but keeps power to essential parts (RAM, CPU). It uses very little power, but if power is lost it wont recover.
I use hibernate all the time. Takes a little longer to boot, but uses no power. Confusingly, Vista has a new hybrid sleep which saves the data to disk like hibernate but then goes into standby. Meaning it can boot instantly like standby, but if you lose power it resumes from the hibernation state. Very clever