A conformal transformation is a mathematical operation that preserves angles but not necessarily distances. This means that while the shape of objects may change, the angles between intersecting lines remain the same. Conformal transformations are often used in complex analysis and geometry to study properties of shapes and spaces. These transformations are particularly important in fields like physics, where they help simplify problems in theory of relativity and fluid dynamics. By using conformal maps, scientists can analyze complex systems more easily, as these transformations maintain the essential geometric structure of the original problem.