Homogeneous coordinates are a mathematical representation used in projective geometry to simplify the handling of points in space. In this system, a point in 2D space is represented by three coordinates (x, y, w), where w is a scaling factor. If w is not zero, the actual coordinates can be obtained by dividing x and y by w, allowing for easier manipulation of points, especially in transformations like translation, rotation, and scaling. This system extends to 3D space as well, where a point is represented by four coordinates (x, y, z, w). Homogeneous coordinates enable the representation of points at infinity, which is useful in computer graphics and robotics for rendering and geometric calculations.