It's a pretty usefully compact definition. In my understanding however, it's valuable to note that the chain-ability of the bind operation also sets up a conti

It's a pretty usefully compact definition. In my understanding however, it's valuable to note that the chain-ability of the bind operation also sets up a continuously nested set of closures, which is where the real power comes into play to give you a useful approximation to imperative programming. (This can easily be abused, of course, to circumvent thinking and structuring code functionally.) Related to this, SJP stressed in a talk some years back about how monads conveniently encapsulate the unavoidable messiness of side-effects in the least painful way yet discovered.