Homotopy equivalence is a concept in topology that describes a relationship between two topological spaces. Two spaces, X and Y, are said to be homotopy equivalent if there exist continuous functions between them that can be "reversed" up to a continuous deformation, known as homotopy. This means that X can be transformed into Y and vice versa without tearing or gluing. In practical terms, if X and Y are homotopy equivalent, they share important topological properties, such as their homotopy groups. This equivalence allows mathematicians to study complex spaces by analyzing simpler ones, making it a fundamental concept in algebraic topology.