A transitive relation is a type of relationship between elements in a set. If an element A is related to an element B, and element B is related to element C, then A must also be related to C. This property is essential in various mathematical contexts, such as in set theory and order relations. For example, consider the relation "is an ancestor of." If person A is an ancestor of person B, and person B is an ancestor of person C, then person A is also an ancestor of person C. This illustrates the transitive nature of the relation.