Curved spaces refer to geometrical structures that bend or curve, unlike flat surfaces. In mathematics, particularly in the field of geometry, curved spaces can be described using concepts from differential geometry. These spaces can be two-dimensional, like the surface of a sphere, or three-dimensional, like the surface of a balloon. In physics, curved spaces are essential for understanding the theory of general relativity, proposed by Albert Einstein. This theory explains how massive objects, like planets and stars, warp the fabric of space and time around them, leading to the phenomenon of gravity.