What is recursion, and what two ingredients does every recursive function need?

Recursion is when a function solves a problem by calling itself on a smaller version of the same problem. Each call handles one slice, then hands the rest to another call.

Every recursive function needs two ingredients. First, a base case: an input small enough to answer directly, with no further call. Second, a recursive step that shrinks the problem and calls itself, moving steadily toward that base case.

Miss either one and it breaks. Without a base case the calls never stop. Without real progress toward it, you also never stop.

A factorial shows both parts clearly:

function fact(n) {
  if (n <= 1) return 1;      // base case
  return n * fact(n - 1);    // shrinks toward base
}
// fact(4) === 24