The theorem states
Let $A$ be a finitely generated $K$-algebra. Then there is a finite algebraically independent set S over $K$ and A is finite over $K[S]$.
I have seen some algebraic geometric interpretation. But can I understand just from aglebraic point of view? (Why is it called normalization?)
A normal domain $R$ is an integral domain which is integrally closed as for the ring morphism $R\hookrightarrow\text{Frac}(R)$. Can I use the theorem to normalize $R$ in its fraction field or something?