Quantization is an important detail, but a bit of a red herring. The main idea is that the same system could have different effective/useful descriptions at different scales of observation. In principle, the idea of renormalization group flow is to be able to go from one description to another, up or down the abstraction ladder. Perfect abstractions might correspond to fixed points of RG flow (I.e. conformal field theories), but the game is all about using the leaks in the abstractions to be able to understand what might be a better model at a different scale.

With specific regards to field theory, this scale dependence becomes much more obvious because we expect the same parametric model (but with different parameter values) to be valid over an enormous range of observation scales. So, we talk about RG flow preserving the model structure, but the couplings/parameters "flowing" or "running".

Almost all the hard/tedious RG calculations are about how to take a description at one scale/abstraction and compute higher-order effects which can be abstracted as a simpler model at the desired level.

Now, in practice, this is very important whenever one has a model with many degrees of freedom (eg: a PDF over image pixels, or a field theory of protons where the pixels roughly correspond to spatial locations). The challenge is to effectively reduce the number of degrees of freedom and derive a useful abstraction to understand (as a scientist) or influence (as an engineer) the system. If this coarse graining / compression is lossy then the transformation is hard/impossible to invert.