Should you leave your computer on while defragmenting?

Yes.

Defragmentation is, as it says on the tin, a defragmentor. what it does is organises the files on your hard-disk. think of it as a set of cards. you place put the most recently used card on top, and after a while, the cards become un-organised, so it takes a lot longer to find the ace of spades. what the defragmentor does is organises the cards so that they are in order, so when you go to look for the 8 of clubs, you know roughly where it is instead of looking through the whole deck.