The idea behind functions is very simple: split up a large program into smaller chunks that can be reasoned more easily and allow the reuse of the code to avoid repetition. This second point is known as the DRY principle: Don't Repeat Yourself. The more the number of times you write the same code, the more the chances you create of a bug creeping in.
When this principle is taken to its logical conclusion, you would have created a program that consists of many small functions, each doing a single thing; this is similar to the Unix principle of small programs, where each program does a single job.
The same principle applies to the code inside a function. Typically, in say Java, a large function or method might be broken down by calling ...