[mbrock]

Another way to say it: a monad is a generic type with the sufficient API to do binding sequences like

    x <- fetch "foo"
    y <- frob x
    return (x + y)

The meaning of binding/sequencing is decided by the particular monad instance. This is why it's a useful formalism to represent things like asynchronous I/O (you make the sequencing mean promise chaining), abortable computations (you make the sequencing cancel when it sees failure values), combinatorial/nondeterministic programming (you make it so one binding can happen several times).

Monads are also closely related to continuation-passing style or delimited continuation capture, and those techniques can also be used to implement everything monads can.