Since the monad structure itself carries some inherent information, that is how "side effect" information can be carried outside of the actual data and be part of the monad structure instead. So e.g. the Maybe monad. It either has data or it does not have data. The information whether carries data or not lives outside the data itself. Or the list monad carries information on how many data points it carries and the order of the data points without that being being part of the actual data it holds.

This is how "side effect" information is carried outside the actual information the monad is carrying. Real side effects like writing to disk however are not real monads. The IO monad pretends to be a real monad but it's not. It just helps with hiding the impurity of IO from the pure parts of Haskell.

So one might think about the IO monad kind of like the list monad where the order of the IO operations is encapsulated. It kind of pretends that the IO part is pure and deterministic when its actually not in order to have a somewhat clean separation between pure and non pure parts of the program.

Hope that helps.