When a program checks the spelling in a document, the program searches for matching words in a dictionary. When a customer enters a title of a book on the Web site of an on-line bookstore, a program on the store's server searches for the price, reviews, and other information that will help the customer decide for or against making a purchase.
Computer scientists have created some of the most complex objects that human beings have ever designed and built. The largest programs contain tens of millions of instructions. If printed on paper and bound in books, a single large program would fill thousands of volumes. No single person can fully comprehend a large program. Large teams work for many years to write large programs. New members join and experienced contributors depart at every stage.
Recursion is a way of solving a large problem by solving smaller but similarly structured problems. Here is an example.
$$ \begin{eqnarray} f(n) & = & n! \\ & = & n \cdot (n - 1) \cdot (n- 2) \cdots 3 \cdot 2 \cdot 1 \\ & = & n \cdot f(n - 1) \\ f(0) & = & 1 \end{eqnarray} $$