When converting formulas to CNF, we replace existentially quantified variables with Skolem functions that depend on surrounding universally quantified variables. For example, in
∀x ∃y p(x,y)
the value of y depends on the particular x, so y will be replaced by f(x).
What if the universally quantified variable was unused in the existentially quantified formula, i.e. is not a free variable in the body of the existential quantifier?
∀x ∃y p(y)
Can we simplify matters by ignoring x completely and just replacing y with a Skolem constant a?
Basically yes, but as sticklers for details we shouldn't literally refer to $p({\bf a})$ as the Skolemization of $\forall x\exists y(p(y))$. Rather, we should say that $\forall x\exists y(p(y))$ is equivalent to $\exists y(p(y))$, and the Skolemization of the latter is $p({\bf a})$ for a fresh constant symbol ${\bf a}$.
This is a bit hair-splitting, but it is the technically accurate way to do things; in particular, there is a serious difference between adding a unary function symbol versus a constant (= nullary function) symbol to a language.