They are interesting in purely functional languages like Haskell because they allow for side effects without sacficicing purity and referential transparency. Rather than allowing side effects, you describe the program as, say, specs for the instruction to run, plus the function that decides what the next instruction is after the first instruction completes and yields a result. Kind of like a linked list of functions that return imperative instructions.

I don't think the general concept is that interesting, at least in programming. Monoids, though simpler, are probably way more interesting (mapreduce, caching, etc)