A coset is a concept in group theory, a branch of mathematics that studies algebraic structures called groups. When you have a group G and a subgroup H, a coset is formed by taking an element g from G and combining it with every element in H. This results in a new set, called a left coset, denoted as gH. Cosets can also be right cosets, which are formed by multiplying the subgroup H on the right side of the element g, denoted as Hg. Cosets help in understanding the structure of groups and are essential in the study of Lagrange's theorem, which relates the sizes of groups and their subgroups.