Ricci curvature is a mathematical concept used in differential geometry to measure how much a geometric space deviates from being flat. It is derived from the more general notion of Riemannian curvature and focuses on the way volumes change in a curved space. Specifically, it captures the average curvature of a manifold by examining how the volume of small geodesic balls differs from that in flat space. In the context of general relativity, Ricci curvature plays a crucial role in understanding the geometry of spacetime. It is related to the distribution of matter and energy, influencing how gravity affects the shape of the universe. The Einstein field equations incorporate Ricci curvature to describe how mass and energy curve spacetime, leading to the gravitational effects we observe.