Riemann Curvature is a mathematical concept used in differential geometry to describe how curved a space is. It helps us understand the intrinsic geometry of surfaces and higher-dimensional spaces by measuring how much the geometry deviates from being flat, like a plane. The Riemann Curvature Tensor quantifies this curvature and can be derived from the metric tensor, which defines distances and angles in a given space. This curvature plays a crucial role in Einstein's General Relativity, where it describes how mass and energy influence the curvature of spacetime, affecting the motion of objects.