Clifford algebras are mathematical structures that extend the concept of real numbers and complex numbers to higher dimensions. They are generated by a set of basis elements that square to give specific values, allowing for the representation of geometric transformations and rotations in various dimensions. These algebras are particularly useful in physics and engineering, as they provide a framework for understanding spinors and quantum mechanics. They also play a role in computer graphics and robotics, where they help model complex spatial relationships and movements.