Functoriality is a concept in mathematics, particularly in category theory, that describes a relationship between different categories. It involves a functor, which is a mapping that preserves the structure of categories, meaning it translates objects and morphisms (arrows) from one category to another while maintaining their relationships. In number theory, the Langlands program is a significant area where functoriality plays a crucial role. It proposes deep connections between Galois representations and automorphic forms, suggesting that properties of one can be translated into properties of the other through functorial relationships.