Welcome to the forum !
The explanation is as follows :
You purchased a nice movie which comes on one DVD9 (That's 9 gigabytes) and you want to backup this movie ONCE, because you don't want your kids to destroy the original. Fair use , fair policy.
However , 9 gigs of dvd information is never going to fit on a single dvd-recordable media (4.5 / 4.7 gigs).
So , you need to either get rid of 4.5 or recompress to get it all fit. This is where DVD Shrink kicks in. AnyDVD is good for getting rid of region codes.
So , you execute DVDShrink , open the original disc and "shrink it". DVDShrink removes the region code , unscrambles the data and recompressed it to a size that it'll fit on a single dvd-recordable.
This backup however can easily be backuped again (WHICH IS FORBIDDEN BY LAW ! You are allowed to make ONE backup) , beause it alread has the correct size and doesn't have any scrambled data anymore.
So yes it's possible and no you may not do it because of the law.
Depending if you copy it "on the fly" or using hard disk caching , writing times may vary from 15 minutes to 45 minutes for a single disc.