<p>On my reading spree, I stumbled upon something called <a href="http://en.wikipedia.org/wiki/Intentional_programming" rel="noreferrer">Intentional Programming</a>.
I understood it somewhat, but I not fully. If anyone can explain it in better detail, please do. Is it being used in any real application?</p>

It appears to be a method of programming that allows the programmer to expand what is actually in the language to more closely follow their original intent, rather than forcing the programmers intent into the constrained syntax of the language.
It explicitly mentions LISP as a language that supports this, so I'd suggest you read up on this great language :) LISP Macros are exactly what are described in the article, allowing you to indefinitely expand the language to cover almost anything you would care to express. (A fairly common outcome of large LISP systems is that you end up with a domain specific language that is very good for writing specific applications, i.e. writing a word processor ends up with a word processor specific language).
For your last part, yes LISP (and thus Intentional Programming) is used in some projects. Paul Graham is a great proponent of LISP, and other examples of it include the original Crash Bandicoot (a game object creation system was created in LISP for this, including a LISP PlayStation compiler)