For instance, in most other programming languages, new abstractions are
built by writing code on /top/ of existing abstractions. But in lisp,
its possible to build new abstractions by writing code *beneath*
existing code.

Here's an example (in scheme):

(define (square x) (* x x))
(define (power x n)
  (cond ((= n 0) 1)
        ((odd? n) (* x (power x (- n 1))))
        (else (square (power x (/ n 2))))))

This is a simple function which raises x to the integer power n, with a
minimum number of multiplications. (let ((x 5)) (power x 3)) returns
125.
Now its possible to make the same piece of code return optimized
symbolic output by just writing a new implementation of '*' !

(power 'x 3)  ->  (* x (* x x))

See the original article by Darius Bacon for the details:
http://cybertiggyr.com/gene/peval/peval.cgi

[sreeram;]