Somebody asked in a now-deleted comment: 'Right, and what does it mean in the context of "A monad is just a monoid in the category of endofunctors"?'

Here is an answer to this question:

What the parent poster referred to are "monoids in the category of sets". You can recognize this as they have introduced the carrier as (just a) set.

But the notion can be generalized. For instance, a "monoid in the category of datatypes" would not be given by a mathematical set and a mathematical binary operation, but by a datatype and a computable binary operation. (To make this precise, I would need to fix which "category of datatypes" I have in mind. It could be the category of Haskell types and Haskell functions, for instance; but C types and functions would work just as well. I could also go all the way to the effective topos, which contains lots of types which most mainstream programming languages are missing such as true quotient types.)

Finally, a "monoid in the category of endofunctors" is given by an endofunctor and a natural transformation. Endofunctors can be pictured as container kinds (e.g. ordered lists, unordered lists, Maybe/Optional, trees, vectors of length n, pairs, ...) and the additional datum of the natural transformation is what singles out those container kinds which support a "flattening operation" from those which don't. For instance, we can flatten a list of lists into one (long) list, but we cannot flatten a pair of pairs into one pair (we would need to drop two of the four elements).

Just as it is quite convenient that many results about integers or lists also hold for all monoids in the category of sets, it is quite nice that many results about monoids in the category of sets also hold for all monoids in all categories and hence in particular to monads.