What is the objective of renormalization group theory?
I would put it this way.
To make renormalization, you first need to do a regularization. Any regularization involves some arbitrary energy-scale parameter, such as the cut off. The physical result should not depend on the choice of the value of that parameter. But this requirement is not trivial at all. It turns out that this requirement has a consequence that some physical quantities depend on energy in a physical process in a specific way. This dependence is what the renormalization group equation describes.