There's a good definition of the word idempotent over on Dictinoary.com. In a nutshell, the word is used to describe mathematical functions that satisfy the relationship f(x)=f(f(x)): functions for which repeated applications produce the same result as the first. For functions that satisfy this condition, you can rest assured that you can apply the function as many times as you like, get the expected result, and not screw anything up if you apply it more times than you absolutely need. This turns out to be a useful concept for people developing software systems.
One of the most common examples of this is in C-style include files. It's common practice to write code like this, to guard against multiple inclusions:
#ifndef __HEADER_FILE_GUARD
#define __HEADER_FILE_GUARD
// ... declarations go here...
#endif __HEADER_FILE_GUARD
This idiomatic C code protects the include file against multiple inclusions. Include files with this style of guard can be included as many times as you like with no ill effect.
The benefit to this is that it basically changes the meaning of the code #include <foo.h> from "Include these declarations" to "Ensure that these declarations have been made". That's a much safer kind of statement to make since it delgates the whole issue of multiple inclusions to a simple piece of automated logic.
Of course, this is pretty commonplace. More is to come...