Birational equivalence is a concept in algebraic geometry that describes a relationship between two algebraic varieties. Two varieties are said to be birationally equivalent if they can be related by rational maps, which are functions that are defined on dense open subsets of each variety. This means that, although the varieties may not be isomorphic (structurally identical), they share many important properties. In practical terms, birational equivalence allows mathematicians to study complex varieties by comparing them to simpler ones. For example, if two varieties X and Y are birationally equivalent, they can often be analyzed using the same techniques, making it easier to understand their geometric and algebraic properties.