Allusion is to make a reference to something, or use something as an example of a thought.
The most important allusion in The Catcher in the Rye is precisely in Chapter 22, as Holden heard the Robbie Burns song: "Coming though the Rye," and Phoebe asks Holden basically what he wants to do with it, and he explains that he sees kids playing in the rye and he wants to be the catcher before they fall off its cliff.
You don't have to read long to find an example of allusion in J.D. Salinger's The Catcher in the Rye. There's one in the opening sentence. Holden Caulfield, the narrator, begins his story with what he is not going to write about: where he was born and how lousy his childhood was and how his parents were occupied before they had him. He sums up what he is not going to write about with an allusion:
...all that David Copperfield kind of crap.
He's alluding to David Copperfield by Charles Dickens. The narrator is not going to write a Victorian-like, Dickens-like, heavy on the description and heavy on the detail portrait of abuses he suffered during childhood. For one, he didn't even tell that personal kind of stuff to his brother when he saw him. Secondly, his parents are nice, though they are quite touchy.
An allusion indirectly references something of literary, cultural, historical, or political significance. In The Catcher in the Rye, Holden Caulfield makes frequent allusions, often to works of literature he has read.
One of these allusions occurs when Holden is sitting in a sandwich bar eating breakfast and two nuns sit down next to him at the counter. A conversation begins between them, and Holden mentions the materials he has read for his English class, including Romeo and Juliet. Holden feels awkward about this conversation since he claims that the play "gets pretty sexy in some parts." He also spends an inordinate amount of time talking about how he doesn't like how someone "very smart and entertaining" (Mercutio) gets killed in the play because of someone else's mistake. Because he doesn't mention Mercurio directly, this is an allusion.