Comment by ndriscoll

It just means if you have some functor F (generic type with a well-behaved `map` function, like List), then you have a `flatten` operation F[F[_]] - > F[_], and like a monoidal product, it's associative. So if you have a triply nested List, you can flatten inside first or outside first. Also, like a monoid, it has an "identity" function wrap: A->F[A] (e.g. x -> [x]). Identity in the sense that "multiplying" (flattening) with wrap does nothing. i.e. wrap(flatten(x)) = flatten(wrap(x)) = x when those things make sense.

So basically wrapping and flattening behave in a sane way. Flatten is your multiply, wrap is your multiplicative identity, and it's like a monoid if you squint.