"What are we to make of this? Does it mean that on a microscopic level the universe operates in ways so obscure and unfamiliar that the human mind, evolved over eons to cope with the phenomena on familiar everyday scales, is unable to fully grasp "what really goes on"? (...) No one knows."

Greene is taking about quantum mechanics, a theory that simply 'worked' to confirm experimental testing, but had no elegance, no logic. This quote isolates the very paradox of objective truth and understanding. While science is the keeper of 'objective truths', they are simply 'tricks' that help predict or regulate reality. It is akin to (and this is my analogy) a definition: if every new word encountered within a definition for some unknown word is to be looked up, then it is simply logically impossible to 'understand' the 'essence' of a word - to know it. And yet humans do communicate. Thus, the problem is with representation: once the subjectively perceived object is represented by an objective symbol (a word), absolute understanding is lost.