What is the purpose of universal quantifier? The universal generalization rule of predicate logic says that whenever formula M(x) is valid for its free variable x, we can prefix it with the universal quantifier, 
M(x) ⊢ ∀x M(x).

But it seems then makes no sense. Why do you introduce a notion that does not mean anything new?

$M(x)$ doesn't strictly have a truth value; $\forall x.M(x)$ does. So, different beasts. Not to mention "$T\vdash M(x)$" is not a sentence in the language, while again, "$\forall x.M(x)$" is.
The universal generalization rule connects a piece of metatheory ("for any variable '$x$', '$M(x)$' is provable", or some such), with a statement in the theory itself. The distinction is a subtle one, and won't often trip one up in everyday logic use, but when studying some truly abstract reaches of logic like model theory, you can end up in some tangled fallacies if you don't keep theory and metatheory apart.
