A Dirichlet character is a special type of arithmetic function used in number theory, particularly in the study of modular forms and L-functions. It is a completely multiplicative function defined on the integers, which means that the value of the character at a product of two numbers is the product of the values at each number. Dirichlet characters are periodic, with a period that divides a certain integer called the conductor. These characters are essential in the generalization of the Dirichlet's theorem on primes in arithmetic progressions. They help in understanding the distribution of prime numbers and are closely related to L-functions, which encode significant information about number-theoretic properties.