Group representations are mathematical tools used to study groups by expressing their elements as matrices. This allows us to analyze the group's structure and behavior through linear transformations in vector spaces. Essentially, a group representation translates abstract group elements into concrete numerical forms, making it easier to work with them. In the context of abstract algebra, group representations help in understanding symmetry in various fields, including physics and chemistry. For example, they can describe how molecules behave under different symmetries, aiding in the study of quantum mechanics and crystallography.