Recursion is the ability of a function to call itself

Simple Example:

int Factorial(int n){
   if (n == 0){
      return 1;
     }
   else {
      int result = n * Factorial(n - 1);
      return result;
   }
 }


See other files for a trace showing how this works with 
Factorial(5). Note that in order to get a revealing trace,
we added some output statements to the code. To get a really
good idea of how recursion works, you should study the program 
and its trace really well.

Any recursive function must have some way of stopping,
otherwise the recursion will go on forever. The code that
stops the recursion can be called the "termination part".
In Factorial, this is:
   if (n == 0){
When this evaluates to true, there are no further recursive 
calls.

In addition, the recursive call needs to somehow "simplify"
the problem in some way, otherwise you're not making progress
and the recursion could go on forever. For instance, if upon
being called with n=5, a (buggy version of the) function called 
itself with 5 as the parameter, then we are not making any 
progress, and infinite recursion is possible. Instead, the
correct function, in trying to solve the problem of n! then
works on (n - 1)! - a simpler task.