How does recursion work in programming?

Recursion is a fundamental programming technique where a function calls itself in order to solve a problem. The correct answer highlights that recursion divides a problem into smaller sub-problems, which is central to how recursive functions operate.

When using recursion, the function processes a complex problem by breaking it down into simpler, more manageable components that resemble the original issue. This process continues until a base case is reached — a condition under which the function can provide a straightforward answer without further recursion.

An example of this can be seen in computing factorials. For instance, the factorial of a number n can be defined in terms of the factorial of (n-1), creating a series of smaller calculations until reaching the base case of 1. When implemented correctly, recursion not only simplifies the structure of the code but can lead to more elegant solutions than iterative approaches in certain scenarios.

Understanding this principle is crucial for designing algorithms that effectively utilize recursion, and it underscores its utility in many programming contexts.