Coxeter groups are mathematical structures that arise in the study of symmetry and geometry. They are defined by a set of generators and relations, which describe how these generators can be combined. These groups can be represented using diagrams called Coxeter diagrams, where nodes represent generators and edges indicate the relations between them. Coxeter groups are closely related to reflection groups and can be used to study various geometric objects, such as polytopes and symmetrical shapes. They play a significant role in areas like algebra, geometry, and combinatorics, providing insights into the nature of symmetry in different mathematical contexts.