The scripts allow to manage a series of patches by keeping track of the changes each patch makes. Patches can be applied, un-applied, refreshed, etc.
The key philosophical concept is that your primary output is patches. Not ".c" files, not ".h" files. But patches. So patches are the first-class object here.
Quilt was originally based on Andrew Morton's patch scripts published on the linux kernel mailing list a while ago, but were heavily modified since then.