If $\varphi$ is a formula with $y$ not free in $\varphi$, then the axiom of comprehension tells us that
$$\forall z \exists y \forall x (x \in y\iff x \in z \land \varphi(x))$$
Wht does $y$ is not free in $\varphi$ exactly mean? Is it just that 'the formula $\varphi$ does not contain a variable $y$' (modulo subsitution to another name)?
Free means not bound by a quantifier. So, the formula $x < y$ has $y$ free. But, $\exists y, x < y$ is not free. The reason this is necessary is because of the quantifier $\exists y$ at the beginning of the Axiom. Since it is bound in $\varphi$, you could just replace it with $w$ or some other variable. If it were free in $\varphi$ it would become bound by the Axiom, and wouldn't have the intended meaning.