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.