Characteristic classes are mathematical tools used in topology and differential geometry to study vector bundles. They provide a way to associate algebraic invariants to these bundles, which can reveal important geometric and topological properties of the underlying space. These classes help classify vector bundles over a manifold, such as tangent bundles or principal bundles. Common examples of characteristic classes include the Chern classes, Stiefel-Whitney classes, and Euler classes, each serving different purposes in understanding the structure and behavior of vector bundles in various mathematical contexts.