This article is about Monoids, not Monads. Monoids are simple. Just imagine a bunch of things, and imagine you can "combine" any arbitrary thing to another thing. The combination has the property of being associative (whatever) and you're only allowed to called it a monoid (otherwise convention says you need to call it a semigroup) if there is also an item (the "identity" or "neutral" element) which when you combine it with any arbitrary item, produces that same item as a result.

Common examples are: strings which you're allowed to combine with concatenation (with the empty string being the "neutral" element). Integers with addition as the combiner is also a monoid that also has a few additional named properties (like commutativity and existence of inverses) but they're still monoids.

By "monad-related concepts" do you just mean abstract algebra? Otherwise, how are monoids and monads related, other than that they are both algebraic structures?

My comment was pretty poorly written, and is probably better understood in terms of just "explanations of things starting with mon-" :-D

The concepts aren't tough, people are just pretty bad at putting themselves in the shoes of a learner, and throw bizarre over-complicated descriptions and examples into the mix when explaining them. The description I gave is someone's tongue-in-cheek stab at these which has stuck with me (unless I'm horrendously off and that is actually someone's legit attempt to describe monads)