Let $\mathcal L$ be a formal language.
Part of defining a proof system $\mathscr P$ for $\mathcal L$ is to specify its axioms.
An axiom of $\mathscr P$ is a well-formed formula of $\mathcal L$ that $\mathscr P$ approves of by definition.
An axiom schema is a well-formed formula $\phi$ of $\mathcal L$, except for it containing one or more variables which are outside $\mathcal L$ itself.
This formula can then be used to represent an infinite number of individual axioms in one statement.
Namely, each of these variables is allowed to take a specified range of values, most commonly WFFs.
Each WFF $\psi$ that results from $\phi$ by a valid choice of values for all the variables is then an axiom of $\mathscr P$.