A recursive function is a function that calls itself in order to solve a problem. It typically breaks down a complex problem into smaller, more manageable sub-problems. Each time the function calls itself, it works on a simpler version of the original problem until it reaches a base case, which is a condition that stops the recursion. For example, calculating the factorial of a number is a common use of recursion. The factorial of a number n is the product of all positive integers up to n. A recursive function for this would multiply n by the factorial of n-1 until it reaches the base case of 1.