[dkarl]

There is a famous quote from a mathematician (maybe von Neumann, don't have it to hand) to the effect that you don't understand mathematics, you just get used to it. That's how monads work. You won't figure them out from thinking through the definition or listening to other people's explanations, but you will start to feel comfortable with them if you use them enough.

A mathematical analogy from introductory analysis is the concept of a dense set. If you're encountering the concept for the first time, it's easy to understand the definition, but it's hard to see why it matters. Then you start using it to solve problems and write proofs, and it's incredibly useful. After a while, you get a feeling about it, an intuition about when it might be helpful, and a facility at working through the technical details of using it. You get used to its power, in a way that feels like understanding. But you don't learn anything that can be passed on in words or symbols. You can't say anything to a beginner to clear up their confusion. You can only point them towards the exercises through which you acquired your understanding. Monads work exactly the same way.