Can someone explain to me what renormalization is? And why General Relativity isn't renormalizable?
'Renormalization' is a catch-all term used to describe mathematical tricks that are used to get finite results by canceling infinities and whatnot.
General relativity does not need 'renormalization', quantum mechanics does.
When you extend quantum mechanics to include gravity (general relativity) the final theory must be re-normalized as a consequence of it's mathematical formulation. With some possible theories (formulations of quantum mechanics including gravity) renormalization tricks will succeed in producing a finite answer (like the electron has X much magnetic moment etc.) but with all of the theories we have tried so far (with the possibly exception of string theory, but they have other problems such as choosing a vacuum) renormalization fails to produce any finite results.
The reasons that renormalization fails to work when you combine quantum mechanics and gravity is just because.