The exterior derivative is a mathematical operation used in differential geometry and algebraic topology. It takes a differential form, which is a type of function that can be integrated over a manifold, and produces a new differential form of a higher degree. This operation helps in understanding the properties of shapes and spaces by capturing how forms change over them. In simple terms, if you have a 0-form (a function), the exterior derivative gives you a 1-form (a differential), which can be thought of as a way to measure how the function varies. The exterior derivative is denoted by the symbol d and satisfies important properties, such as linearity and the property that applying it twice results in zero, d(d\omega) = 0 for any form \omega.