I, too, did not find this very understandable when I was trying to learn Lambda Calculus for the first time. Even now, it is still quite baffling how alligators eating aligators makes more intuitive sense than the regular notation (well, at least it's recursive). In the end, I was only really able to grasp Lambda Calculus from reading a hard book.
Frankly, I think the best way to learn lambda calculus is by writing code in Scheme or Common Lisp or some other language with a nearly one-to-one mapping between the language's syntax and semantics and what lambda calculus has. Learn by doing, in other words, and introduce hard concepts using code.
Yes, that's SICP. It's pretty much inevitable that book would get mentioned here, because there's a whole group of people (not everyone) who learn best when they learn by doing, and SICP is the paradigmatic contribution of the learn-by-doing school to this topic.
My point is, maybe this alligator stuff could be made into a game and people could learn by playing. That's a well-verified method.
