What is it used for?
To get the girl comfortable with being naked, including the ability to strip and clothe her (at will, eventually).
What exactly is the purpose of "nude" training?
To improve her 'naked' preference score, and maybe some other stats as a byproduct. You can always do some less conventional things as well, like making a reluctant girl train nudity, then punish her for it. Or have Gizel do nudity training as a preparation.
What is improved by training it?
Naked preference, obedience, libido, body, love/fear/mood.
If you mean what it's ultimately good for, 1) eye candy and 2) a moderate boost to income from girls who performing a non-sexual job while naked.