The poem "There Will Come Soft Rains" by Sara Teasdale shares its title with the short story by Ray Bradbury because it is recited by the house to entertain one of the inhabitants. Unfortunately, the inhabitants are all dead, killed in a nuclear explosion with the rest of the city. The house cannot know this, because all of its functions are automatic, and so it simply continues on its programmed schedule.
There will come soft rains and the smell of the ground,
And swallows circling with their shimmering sound;
And not one will know of the war, not one
Will care at last when it is done.
Not one would mind, neither bird nor tree,
If mankind perished utterly;
(Bradbury, "There Will Come Soft Rains," from Teasdale, "There Will Come Soft Rains," nexuslearning.net)
The bolded phrase shows how Bradbury took one meaning of the poem and used it in his story; at least one city has been destroyed by nuclear war, but the house, less intelligent than even an animal or bird, doesn't know or care that its inhabitants are dead. It continues to perform its automated tasks without any larger purpose, and eventually is destroyed by a smaller fire, echoing the enormous fire that killed the people. The themes of both story and poem are similar, but the poem is a little more optimistic than the story, as it shows how nature will continue after humanity dies out; the story shows how even humanity's great innovations will be destroyed with time, leaving no trace of their existence.