People have different "aha" moments with monads. For me, it was realizing that something being a monad has to do with the type/class fitting the monad laws. If the monad laws hold for the type/class then you've got a monad, otherwise not.

So then when you look at List, Maybe, Either, et al. it's interesting to see how their conforming to the laws "unpacks" differently with respect to what they each do differently (what's happening to the data in your program), but the laws are just the same.

The reason this was an aha moment for me is that I struggled with wanting to understand a monad as another kind of thing — "I understand what a function is, I understand what objects and primitive values are, but I don't get that List and Maybe and Either are the same kind of thing, they seem like totally different things!"