The Curvature Tensor is a mathematical object used in differential geometry to describe the curvature of a space. It provides a way to quantify how much a geometric space deviates from being flat. In the context of Riemannian geometry, the curvature tensor helps in understanding the intrinsic properties of surfaces and higher-dimensional spaces. In general relativity, the curvature tensor plays a crucial role in describing the gravitational field. It relates the geometry of spacetime to the distribution of mass and energy, encapsulated in Einstein's field equations. This relationship allows physicists to understand how massive objects like stars and planets warp the fabric of spacetime around them.