In literature, an epigraph is an introductory quote taken from one piece of literature and used at the beginning of another piece of literature. The purpose of the epigraph is to illuminate, in one way or another, the objective or meaning or mood etc of the piece of literature in which it is quoted. For instance, a novel about choosing virtuous behavior in the face of great unmet need might be introduced with this epigraph quotation from Plato: "All the gold which is under or upon the earth is not enough to give in exchange for virtue."
An epigraph may perform a number of functions that illuminate a text. (1) It may set-up intertextual comparisons or contrasts. For instance, hypothetically speaking, Tales of King Arthur may be prefaced with an epigraph from Machiavelli's The Prince to establish a contrast between two philosophies in the reader's mind. (2) It may serve as a preface to the chapter or story or novel by establishing the purpose or scope the upcoming text. For instance, a chapter on apartheid might be prefaced by this epigraph from Deuteronomy 32:28: "For they are a nation void of counsel, / And there is no understanding in them."
(3) An epigraph may act as a summary of the upcoming text. For instance, a novel about a talented and successful young woman whose failing was being self-centered and unperceptive might be summarized by this epigraph from Jane Austen's Emma: "The real evils, indeed, of Emma's situation were the power of having rather too much her own way, and a disposition to think a little too well of herself; these were the disadvantages which threatened alloy to her many enjoyments." (4) It may provide a contrasting, countering perspective to the upcoming text. For instance, an essay against free-trade agreements may open with this contrastive quote from John Adams' Wealth of Nations: "To widen the market and to narrow the competition, is always the interest of the dealers…"