Gaussian curvature is a measure of how a surface bends in different directions at a given point. It is calculated using the product of the principal curvatures, which are the maximum and minimum curvatures of the surface. A surface can be classified as having positive, negative, or zero Gaussian curvature based on these values. For example, a sphere has positive Gaussian curvature because it curves outward in all directions. In contrast, a saddle shape has negative Gaussian curvature, as it curves up in one direction and down in another. Flat surfaces, like a plane, have zero Gaussian curvature, indicating no bending.