Euler's Theorem states that if two numbers, a and n, are coprime (meaning they have no common factors other than 1), then raising a to the power of φ(n) will yield a result that is congruent to 1 modulo n. Here, φ(n) represents Euler's totient function, which counts the integers up to n that are coprime to n. This theorem is a fundamental result in number theory and has applications in areas such as cryptography, particularly in algorithms like RSA. It helps in simplifying calculations involving large powers in modular arithmetic, making it easier to work with large numbers.