Stiefel-Whitney classes are a set of topological invariants used in the field of differential topology to study the properties of vector bundles. They provide a way to classify bundles over a manifold, helping to understand how they can be twisted or arranged. Each class is associated with a specific dimension and can be computed using characteristic classes. These classes are particularly important in algebraic topology and have applications in various areas, including theory of manifolds and cobordism. The first Stiefel-Whitney class, for example, can indicate whether a vector bundle is orientable, while higher classes provide deeper insights into the bundle's structure.