The gamma function is a mathematical function that extends the concept of factorials to non-integer values. For positive integers, the gamma function is defined as Γ(n) = (n-1)!, meaning that it produces the factorial of a number minus one. For example, Γ(5) equals 4! or 24. The gamma function is defined for all complex numbers except for non-positive integers. It is often used in various fields such as statistics, probability theory, and complex analysis due to its useful properties and relationships with other mathematical functions, including the beta function.