Ricci Flow is a mathematical process used in differential geometry to smooth out the shape of a manifold. It involves evolving the metric of the manifold in a way that reduces irregularities, similar to how heat diffuses over time. This flow is governed by a partial differential equation that describes how the curvature of the manifold changes. Developed by Richard S. Hamilton in the 1980s, Ricci Flow has significant implications in the study of geometric structures. It gained widespread attention when Grigori Perelman used it to prove the Poincaré Conjecture, a major problem in topology, demonstrating its power in understanding the shape and structure of spaces.