Monoids really are simple things. Monads are a bit less so, but they're still fairly simple objects (as evidenced by the fact that they have a short description, "monoids in the category of endofunctors", even if most people don't know what that means).

Adjunctions turn up all over maths, but I've been trying for a while to come up with an example which programmers (as opposed to mathematicians) would quickly understand. Broadly speaking, they represent "the leanest way to add a particular structure to something", but of course that's pretty useless for understanding them!