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 help in understanding the distribution of prime numbers in arithmetic progressions. Dirichlet characters can be either principal or non-principal. The principal character corresponds to the case where all integers coprime to n are mapped to 1, while non-principal characters take on values in the complex numbers, often revealing deeper properties of numbers. They play a crucial role in analytic number theory and have applications in cryptography.