A Dirichlet character is a special type of arithmetic function used in number theory, particularly in the study of Dirichlet L-functions. These characters are defined modulo some integer n and are completely multiplicative, meaning the value of the character at a product of two numbers is the product of the values at each number. They take on complex values and are periodic, repeating their values after a certain interval. Dirichlet characters play a crucial role in analytic number theory and are instrumental in proving results like the Dirichlet's theorem on arithmetic progressions. They help in understanding the distribution of prime numbers in different residue classes and are essential in the study of modular forms and Galois representations.