Having been mildly disappointed by the simplicity of monoids, after intimidation from the complexity in maths, i expect that something like an adjunction is something already known to a commoner in any case, just that the vocabulary, particaularies and relations to the concept in question are not always obvious.
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!
