Optimal beta reduction is a very technical term. In effect it means any "family" of lambda terms will all be reduced "at once." What is a family? Go take two semesters in rewriting theory and then perhaps our two heads together can pin it down exactly.

In laymen's terms, it means that you're doing a variant of call-by-need, except you can be absolutely sure you don't copy applications without need.

I am personally skeptical it's a useful idea at all. Machine computation is what we really care about (how fast can you push instructions through the pipeline) and graph reduction systems were already all the rage in the 80s. We gave up on them because they didn't interact with the cache well.

So, this is the "motherload" of all graph reduction strategies, yet it will get absolutely trounced in settings like numerical computation.