It's hard to understand because it's utterly unenlightening. It's a restatement of the definition. It's like saying "the number two is just the sum of one and one." It's trivially true yet utterly fails as an explanation because it requires more concepts to convey the exact same content.
I would argue the concepts of monoid objects and the category of endofunctors on an object are simpler than that of monads, so this description does help. I come from a math background and had never seen this quote before, and I think it has given me a definition of (mathematical) monads that I can remember.
Haskell, unfortunately, is still quite opaque to me.
http://stackoverflow.com/questions/3870088/a-monad-is-just-a...
But I didn't really try to understand it.