The Y combinator is an infuriating construct used to write recursive functions with pure lambdas (confused already? read this first). But unfortunately it appears that reading an explanation of the Y is somewhat recursive too. You don't get it unless you already get it. My own exposition assumes a basic knowledge of Scheme and is probably no worse than several others.
Constructing Y (scheme source)
My plan is to write other explanations, so that the reader may enjoy being confused in several different ways. Stay tuned.