A finite field, also known as a Galois field, is a set of numbers that contains a finite number of elements, where you can perform addition, subtraction, multiplication, and division (except by zero) while still staying within the set. Finite fields are commonly denoted as GF(p^n), where p is a prime number and n is a positive integer. These fields are essential in various areas of mathematics and computer science, particularly in coding theory and cryptography. For example, RSA and AES encryption methods utilize properties of finite fields to secure data.