This is a rather unique story for a number of reasons, the first one being the complete absence of any form of human characters. The only "life" we are presented with is in the form of the robots that humans made before their extinction and then the few straggling examples of nature that remain, such as the dying dog. However, the title is explictly linked to the central conflict of the story, which is indicated through the allusion to the poem by Teasdale. We see nature and mankind set in conflict with each other, but the overwhelming message of the story is the way in which that nature is so much stronger and powerful than mankind, which it has already outlasted. Note the following quote from the poem:
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:
And Spring herself, when she woke at dawn
Would scarecely know that we were gone.
Ironically, the robot has chosen to read a poem that sums up precisely the scenario that we are presented with. Mankind has "perished utterly," but nature carries on regardless. In spite of our feelings of lofty grandeur, we are incredibly forgetable, and when we perish, nature will continue without even noticing our absence. We will have failed to leave a mark on the cosmos in the large scheme of things. In spite of the massive technological advances that man has been shown to make in this story, we still have not gained for ourselves immortality.
The title is reflective of Teasdale's poem of the same name. The larger implications is the idea that the condition of nature is a powerful one. Similar to the natural setting of the poem, where a "soft rain will fall" regardless of context and consequence, Bradbury's short story reveals that nature is too large of a force to stop. Human beings cannot overcome the natural condition that has given birth to the world before them and will be present after them. While science and technology has created impressive elements, such as the automated house, the cleaning mice, and the weapons capable of causing great damage, it cannot eliminate nature. It cannot get rid of the natural setting that encompasses all existence and because of this regardless of what happens, "there will come soft rains." In this assertion in both the title and theme, its relevance is evident.