This is not answer to Your question in whole generality, I suggest You take a look in this simple but in my opinion meaningful example of renormalization in simple situation: http://arxiv.org/abs/patt-sol/9709003 "Uses of Envelopes for Global and Asymptotic Analysis; geometrical meaning of renormalization group equation" Teiji Kunihiro and other papers by same author on arxiv.

While it may be generalized to more practical situations it gives also a hint what is it about in elementary way.