p-adic fields are a type of number system used in mathematics, particularly in number theory. They extend the idea of rational numbers by introducing a new way to measure distances, focusing on the divisibility by a prime number p. This allows mathematicians to study properties of numbers that are not easily visible in the usual real number system. In p-adic analysis, numbers are represented in a series that converges based on powers of p. This leads to unique arithmetic properties and helps solve problems related to Diophantine equations and algebraic geometry. Overall, p-adic fields provide a powerful tool for understanding the structure of numbers.