The p-adic metric is a way to measure distances in the field of p-adic numbers, which are a special type of number used in number theory. Unlike the usual distance we use in real numbers, the p-adic metric focuses on the divisibility of numbers by a prime number p. In this metric, two numbers are considered close if their difference is divisible by a high power of p. In the p-adic metric, the distance between two numbers is defined based on how many times their difference can be divided by p. This leads to a unique topology, where sequences can converge in ways that differ from traditional real number sequences. The p-adic metric is essential for various applications in algebraic number theory and has implications in areas like cryptography and mathematics.