I'm inclined to say that some people 'just get' certain things like this or complex SQL. How they got to 'getting it', I don't know.
Perhaps their talent is actually just an attraction to studying it really hard. I, for instance, do not have the patience to study regex so much as to ever get the point where I could easily answer this question.
"To understand monads, you first need to understand monads."
They are an abstraction, effectful computation is not inherent to them, they represent computational contexts, e.g. the list monad is used to model non-determinism, the maybe monad represents computations that can fail, both of these are pure.
This is an excellent set of posts for building an intuition about monads: http://mvanier.livejournal.com/3917.html
See this is the kind of thing that made learning Haskell so hard for me. I'm not a math guy, I'm terrible at math. I have no idea what "non-determinism" means, and I'd venture to guess that list monad is used to model "ordered collections of things".
But the idea of a list also suggests an ordering to me.
I'm fairly certain that in this context, non-determinism means that there can be more than one answer/result.
If you have a `Stream<Deck> decks;` of card decks, and want to get all the cards from all the decks, you might try to do something like `decks.map(deck -> deck.getCards().stream())`, but that will give you the type `Stream<Stream<Deck>>`. That sucks, we just want a single stream, not a stream of streams, so we call the function that flattens at the same time. `decks.flatMap(deck -> deck.getCards().stream())`.
Nondeterminism is just a standard use for this construction: given one choice, generate more choices, given that choice, generate more choices, do some computation with the choices, and then return the list of possible final results.