An epigraph is a sentence, usually a quotation from another literary work or a passage from a famous speech, that is set at the beginning of a novel or a document. The function of the epigraph is to introduce the reader to the themes of the text that they are about to read.
In Atwood's The Handmaid's Tale there are three epigraphs. The first comes from Genesis 30:1-3 and refers to the practice of ancient Hebrew male to get their slaves pregnant if their wives were not fertile. The epigraph introduces the theme of sterility and relates to the right of the novel's totalitarian government to appropriate fertile women's bodies for state controlled child-bearing programs.
The second epigraph is from Jonathan Swift's satire A Modest Proposal (1729). In this famous piece, whose full title reads A Modest Proposal For Preventing the Children of Poor People in Ireland from Being a Burden to Their Parents or Country, and for Making Them Beneficial to the Publick, Swift paradoxically suggests that, to solve the problems of poverty, starvation and overpopulation that were affecting Ireland at the time he was writing, the Irish could eat their own children or sell them. This is obviously an ironic argument. Yet, Swift is able to argue convincingly and logically even the most absurd ideas. Like the Atwood's novel, this second epigraph is concerned with children. Unlike the novel, however, it is about the fact that there are too many children. In addition to these thematic concerns, the epigraph and the novel share the idea that even the most horrible ideas can be given rational legitimacy.
Finally, the third epigraph is a Sufi proverb:
In the desert there is no sign that says, Thou shalt not eat stones.
Sufism is an oriental philosophy that argues for a less wordly Islam. The application of the proverb to the novel has puzzled readers and caused much debate. What Atwood seems to be getting at here is that when something is obviously wrong (such as eating stones or breeding women), we shouldn't need signs or laws prohibiting it.