A Bezier curve is a mathematical curve used in computer graphics and related fields to model smooth curves. It is defined by a set of control points, with the simplest form being a linear curve defined by two points. More complex curves can be created using additional control points, allowing for intricate shapes and designs. Bezier curves are widely used in vector graphics software, animation, and font design due to their ability to create smooth and scalable shapes. They provide designers with precise control over the curve's shape and can be easily manipulated by adjusting the position of the control points.