Actually, formatting is more like deleting the index, making the disk look like empty and thus make it reusable. Nothing is totally deleted until you save something new over the old one. If you're old enough to remember how to reuse C-cassettes by putting a piece of adhesive tape over the gap in the bottom, the idea is pretty much the same.
And yes, as Gyrene said, it makes the disk compatible with the current system. Formatting for compatibility is not necessary, though, when moved from one Windows-machine to another. Think about removable disks, formatting them every time they are connected in a new computer would destroy the whole idea of using them.
