At clothes stores they have arrangements with three mirrors hinged together. If you keep the side mirrors pointing outward, and you're standing in the right position, what you see is just three separate images of yourself, one face-on and two with profile views. But if you turn the mirrors in toward each other, all of a sudden you see what looks like infinitely many images of yourself. That's because each mirror reflects a scene that includes an image of the mirror itself. This self-reference gives rise to the multiple images.
Recursion is the idea of self-reference applied to computer programs.
We make a guess, and if it's not the answer, we use that guess to create another problem in which the same secret number is known to be within a smaller range. The self-reference of the problem description is expressed in Scheme by a procedure that invokes itself as a subprocedure. Actually, this isn't the first time we've seen self-reference in this book.