# What is meant by “the superpotential is not renormalized”?

because of the non-renormalization theorems the superpotential is not renormalized.

I would like someone to be more explicit on what is meant by this sentence. For concreteness sake, let's consider a theory with only a chiral superfield and with superpotential $$W(\Phi)=M\Phi^2+\Phi^3$$ so, what are the consequences of the non-renormalization theorems for the different vertices of this theory?

The important consequence is that there are no quadratic divergences for a mass in the superpotential - there are only logarithmic correction. The $\mu^2\phi^2$ operator is safe from large radiative corrections from, for example, the Planck scale.
Because $\mu^2$ ultimately sets the scale of EWSB (along with a few other soft-breaking parameters), this is very important. It's closely related to how supersymmetry solves the hierarchy problem.