A Cayley graph is a visual representation of a group, which is a mathematical structure consisting of a set of elements and an operation that combines them. In a Cayley graph, the vertices represent the elements of the group, while directed edges connect these vertices based on the group's generators. This helps illustrate the group's structure and relationships between its elements. Cayley graphs are useful in various fields, including group theory, combinatorics, and computer science. They can help analyze properties of groups, such as connectivity and symmetry, and are often used in algorithms and network design to understand complex systems.