An allusion is a reference within a work of literature to history, religion, other literature, or anything within the culture really. Today, references to pop culture including celebrities and TV are common. The most obvious example of allusion in this story is the title, taken from the Sara Teasdale poem which the house recites. ''There Will Come Soft Rains" was written in response to World War I. Teasdale believed that after all the wars were over, the earth would continue to exist without human interference. Though Teasdale could not have imagined the devastation of nuclear war, her poem is the basis for Bradbury's apocalyptic vision. Even a world which has been poisoned will continue to exist. That the house reads this version of the future that has already come to pass is the irony of the situation. Even though the destruction was foreseen, it wasn't prevented.
One other example of allusion, although not as important as the title, is evident in the story. While explaining how the mice clean the house, the speaker describes them feeding the debris into an incinerator which sits "like evil Baal." This is a reference to the heathen god of the Old Testament and Satan's chief lieutenant in Paradise Lost by Dante. This suggests the resulting evil of man's reliance on technology, & the consequences of unregulated advancements.