Zermelo's well-ordering theorem states that every set can be well-ordered, meaning that its elements can be arranged in a sequence where every non-empty subset has a least element. This theorem is significant in set theory and is foundational for various mathematical concepts, including ordinal numbers and transfinite induction. The theorem relies on the Axiom of Choice, a principle in mathematics that asserts the ability to select elements from sets. While the Axiom of Choice is controversial, Zermelo's theorem has been widely accepted and is essential for understanding the structure of infinite sets and their properties in set theory.