The Button referred to in the title is the button that will launch the nuclear missiles in a war. Captain Stone has the key which unlocks the control panel, giving access to the Button. Captain Stone also has nightmares about the nuclear holocaust that would result, should he ever have to push the Button; in his nightmare, his men hold him while one of the sergeants takes his key, and presses the Button, unleashing the nuclear missiles.
Captain Stone wakes up, relieved it was all a bad dream. But just then, the exact same men that were in his nightmare show up-- including the sergeant who took his key and pushes the Button. Was it a nightmare, or a vision of what was to come?