Differential forms are mathematical objects used in calculus and geometry to generalize the concept of functions and integrals. They provide a framework for integrating over various dimensions, allowing for the analysis of curves, surfaces, and higher-dimensional spaces. Differential forms can be manipulated using operations like exterior differentiation and wedge products, making them essential in fields such as differential geometry and theoretical physics. In essence, a differential form can be thought of as a way to encode information about a space and its properties. They are particularly useful in Stokes' theorem, which relates the integration of forms over a manifold to the integration over its boundary, bridging local and global perspectives in mathematics.