[carbonica]

Monads, in the context of programming, are used as abstractions for computation. That's all - some people mention state, because some useful computational strategies maintain state - but not all do. In Haskell:

The List monad represents nondeterministic computation. Each possible result from the previous step in the computation is fed into the next step of the computation.

The Maybe monad represents computation that can fail. If one step of the computation fails, then the rest fail. The previous step of the computation is only fed into the next step of the computation if it succeeds.

The IO monad represents globally stateful computation. The entire state of the program is fed into each step of the computation. Kind of. That's sort of the idea, anyway - it's a model.

The Reader monad represents computation in the scope of a single shared bit of data.

Only the latter two mention state. The idea of monads in programming is just abstracting computational strategies, and sometimes those strategies require or provide state.

Monads are neat in Haskell/ML because you can write code that works on arbitrary monads. Think of it this way: you know how you can write code that operates on a `List` in Java, and it will work on `ArrayList` and `LinkedList`? Well in Haskell, you can write code that operates on/with a given function regardless of computational strategy used.