D-modules are mathematical structures used in the field of algebraic geometry and representation theory. They provide a way to study systems of linear differential equations and their solutions. Essentially, a D-module consists of a module over the ring of differential operators, allowing mathematicians to analyze how functions behave under differentiation. These structures are particularly useful for understanding the relationships between algebraic varieties and their associated differential equations. By using D-modules, researchers can explore deep connections between geometry, analysis, and algebra, leading to insights in areas such as singularity theory and characteristic classes.