Character sheaves are mathematical objects used in representation theory, particularly in the study of Lie groups and algebraic groups. They provide a way to associate a sheaf of functions to a group, capturing information about the group's representations through their characters, which are traces of the group elements' actions on vector spaces. These sheaves allow mathematicians to analyze how representations behave under various operations, such as taking direct sums or tensor products. By studying character sheaves, researchers can gain insights into the structure of modular representations and the relationships between different representations of a group, enhancing our understanding of symmetry in mathematics.