The Stiefel-Whitney class is a fundamental concept in topology, specifically in the study of vector bundles. It provides a way to classify the types of vector bundles over a manifold, helping to understand their geometric properties. The Stiefel-Whitney classes are cohomology classes that can be computed using characteristic classes, which are important tools in differential geometry. These classes are particularly useful in algebraic topology and have applications in various fields, including physics and engineering. They help in determining whether a manifold is orientable and can also be used to study the intersection properties of submanifolds.