An allusion is an indirect reference to something outside the immediate context of the present discourse. For example, in moaning to your grandmother about the state of your bank account, you might remark that it's as depleted as Great Uncle Billy's back forty back in the Dust Bowl. This is a simile, of course, but it won't make any sense to someone who doesn't already know what the Dust Bowl is. And if your grandmother has memories of Uncle Billy's miseries in those days, what you say will take on a vividness that it probably wouldn't for people who weren't there, or who haven't heard their tales of woe.
An example like this reminds us that allusions often depend on a shared body not just of experience but of experience mediated by a common stock of stories. They are dependent, for their work, upon communities that are familiar not so much with the same vocabulary but with a body of standard narratives, that circulate and recirculate. So, many of you will have no difficulty of making sense of a remark like "His wits are as dried up as the Wicked Witch of the East," or (speaking of a politician on election eve) "Let's hope tomorrow we can say Hasta la vista, baby." But others, who've never heard how the tornado sets down Dorothy's house in The Wizard of Oz or had the pleasure of watching Arnold Schwarznegger do his work in The Terminator, may understand the words, but will be left agog as to what's being said. It is true that a huge load of commonplaces consists of allusions, some of which can take on a life of their own and become intelligible to people who've learned them independently of any familiarity with their origins. Consider "I think that's a Micky Mouse idea." If the time ever comes when kids don't grow up on this part of the Disney fare, chances are that this will still survive, at least for a while, as a sensical idiom for a lot of Americans, and maybe even Englishfolk and English-speaking Bangladeshis. But in general, allusions depend for their force on a common domain of reference.
This is sort of like playing tennis against a backboard with someone else: you bounce the ball off the board out away from you, and your partner (or opponent) "picks it up" and returns it. You are "playing to" the backboard by bouncing something off of it in such a way that it comes back into the playing area bringing with it a novel angle or "spin." (In fact, the Latin term "alludire," compounded of ad [to] and ludire [to play], means "to play to," and by extension, "to play off of.")
Sometimes we resort to allusions as a sort of code that is meant to exclude some from understanding at the same time it cuts others in. This isn't always snobbery. Parents may want to share thoughts with each other in front of their children that they don't particularly want the kids to pick up on, and (unless they share a second language the children don't) allusion often offers a way through the minefield. But often allusion can do powerful work beyond this sort of communication-under-censorship. Writer's can use allusion to invite readers to import a rich body of already-established connotation into the context of some scene they are presenting to our imagination. And, historically in European literature since the Middle Ages, the most prominent source of allusions has been the Old and New Testaments and, beyond these, to a famous body of religious literature (ranging from sermons to religious allegories).
Even a writer like Ernest Hemingway, who would surely qualify as an unbeliever in religion, was fond of allusions to the Bible. The title of the novel The Sun Also Rises comes from the King James Version (1611) of the Old Testament Book of Ecclesiastes, which expresses the weary despair at the spectacle of the world's processes imagined as endlessly repeating without any transcendant purpose (the sun rising, and going down; the monotonous circuits of the winds, generations following generations, etc.) Much later in that book, the voice of "the Preacher" asks, "What gain has the worker from his toil?" The reader who is aware that this book of the Bible is often seen as a compilation of two very different texts -- one by a weary skeptic and another, supplied as a frame to it, by a fervent believer determined to convert the skeptic's utterance to pious purposes -- is set to appreciate Hemingway's choice of phrase, and to follow the prompting which this framing provides for the story that the author attaches to it, which turns out to be a powerful expression of the disillusionment that settled upon many, including Hemingway himself, in the wake of The Great War.
After the Bible, as a source of allusion in European (including English) literature, comes Greek and Roman mythology -- at least until recently. When Alexander Pope illustrates the way sound can reinforce sense in skillful verse, one of the couplets he deploys is
- Ajax! -- Boom, boom! --
- the foaming cleanser
- da-da-da-da dah dah
- sweeps the dirt
- right down the drain!
- da-da-da-da-da da
Sometimes allusions are used to call to the reader's mind whole (other) stories, with their own themes. The point of doing this is to pose 2 questions: Do we have to do here with parallel situations (the situation alluded to functioning as a metaphor for the story from within which it is being called up)? Or do we have to do with contrasting situations (so that the situation being alluded to functions ironically, i.e., as a foil to the situation it is being invoked to clarify? Either way, it can alert us to notice aspects built into the present story that we might otherwise be inclined to overlook, or to overlook the significance of.