de Rham cohomology is a mathematical tool used in the field of differential geometry and algebraic topology. It studies the properties of smooth manifolds by examining differential forms, which are mathematical objects that can be integrated over these manifolds. The main idea is to classify these forms based on their ability to be differentiated and integrated, leading to the concept of cohomology classes. The de Rham cohomology groups are defined as the quotient of closed forms (those whose exterior derivative is zero) by exact forms (those that are the exterior derivative of another form). This classification helps mathematicians understand the topological features of manifolds, such as holes and voids, providing insights into their structure and behavior.