Scalar curvature is a mathematical concept in differential geometry that measures how a space curves at a particular point. It provides a single number that summarizes the curvature of a manifold, which is a generalization of surfaces. In simple terms, scalar curvature helps us understand how a shape bends or twists in different directions. In the context of Riemannian geometry, scalar curvature is derived from the Riemann curvature tensor, which describes the intrinsic curvature of a manifold. Positive scalar curvature indicates that the space is locally shaped like a sphere, while negative scalar curvature suggests a saddle-like shape. This concept is essential in various fields, including general relativity and theoretical physics.