Bezier surfaces are mathematical representations used in computer graphics and design to create smooth and flexible shapes. They are defined by a set of control points, which influence the surface's curvature and form. The surface is generated using Bernstein polynomials, allowing for precise manipulation of the shape by adjusting these control points. These surfaces are widely used in various applications, including CAD (Computer-Aided Design), animation, and 3D modeling. By providing a way to represent complex shapes with a relatively small number of points, Bezier surfaces enable designers to create intricate designs efficiently while maintaining a high level of control over the final appearance.