Riemannian curvature is a concept in differential geometry that measures how a curved space differs from flat space. It is derived from the Riemannian metric, which defines distances and angles on a manifold. The curvature can indicate how much the geometry of the space deviates from that of Euclidean space. There are different types of curvature, including Gaussian curvature and Ricci curvature, each providing insights into the shape and structure of the manifold. Riemannian curvature plays a crucial role in understanding the geometric properties of spaces, influencing theories in physics, particularly in general relativity.