Schubert varieties are specific subsets of a Grassmannian, which is a space that parameterizes all linear subspaces of a given dimension within a larger vector space. Each Schubert variety corresponds to a particular way of choosing these subspaces, defined by certain geometric conditions. They play a crucial role in algebraic geometry and have applications in various areas of mathematics. These varieties are named after the mathematician Hermann Schubert, who developed a systematic way to study them in the 19th century. Schubert varieties are often used to understand intersection theory and can be described using Schubert calculus, a method that involves counting intersections of these varieties in a systematic way.