The factorial function is a mathematical operation that multiplies a positive integer by all the positive integers less than it. It is denoted by an exclamation mark, for example, the factorial of 5 is written as 5! and calculated as 5 × 4 × 3 × 2 × 1, which equals 120. The factorial function is defined only for non-negative integers, and by convention, 0! is equal to 1. Factorials are commonly used in various fields, including combinatorics, probability, and statistics. They help in calculating permutations and combinations, which are essential for determining the number of ways to arrange or select items. The factorial function grows very quickly, making it useful for understanding complex mathematical concepts.