Axioms allow you to choose which statements are true in a formally defined system (like ZF set theory or euclidian geometry). Examples like the axiom of choice or parallel postulate require faith in their truth value for any of the statements that follow those axioms to be true.

Any system of reasoning requires some statements be true, and axioms are those bedrock statements that are taken as truths because we require no proof for them. We require no proof because we have faith they are true.