The Fraenkel-Mostowski method is a technique in set theory used to construct models of certain mathematical structures. It combines elements from the Fraenkel and Mostowski approaches to create models that can demonstrate the consistency of various set-theoretic axioms. This method is particularly useful in the study of infinite sets and cardinal numbers. By employing this technique, mathematicians can explore the properties of sets and their relationships, leading to a deeper understanding of foundational concepts in mathematics.