The central conflict in this story is that of nature versus human technology. As the Sara Teadsdale poem that the story's title alludes to suggests, when technology gets into a conflict with nature, nature wins.
In the story, a nuclear holocaust has seemingly wiped out civilization. A single house is left standing, though the family that lived it has been killed. The house is quite technologically advanced and mechanically goes about its duties of caring for the family even though there is no family left to care for. It makes meals, sets up card tables, cleans, and even recites a Sara Teasdale poem. However, when a tree crashes, starting a fire, it is nature that wins—the house burns up and all its smoke alarms and sprinklers can't save it.
The poem and the story warn us that our technology cannot overpower nature nor save us from our fate. We need to control our technology rather than let it control us. We need to align ourselves with nature or we may very well wipe ourselves out—and nature will go on, completely indifferent to our fate.
Bradbury cautions against over-reliance on technology, implying it will lead to our doom.