The Catcher in the Rye is narrated by Holden Caulfield in the first person point of view. The reader gets the events from Holden's perspective and because the narrative does periodically use stream of consciousness, the reader gets a deeper insight into Holden's thoughts. This is significant to the title because in Chapter 22 Holden reveals one of his ideal aspirations. He is quite open about his disdain for the phoniness of adults. This causes the reader to consider the 17-year-old Holden, on the brink of adulthood, as someone who wants to avoid growing up, and one who wishes for the wisdom of an adult but with the innocence of a child.
In Chapter 22, Holden reveals this dichotomy.
What I have to do, I have to catch everybody if they start to go over the cliff--I mean if they're running and they don't look where they're going I have to come out from somewhere and catch them.
Holden envisions himself as a protector of children. His dilemma is that this is an older, or adult, role. Holden reveals this to Phoebe, so this is presented in dialogue. But Holden's narration of the other events during this three-day adventure of his life support this paradox. This is one of the enduring, endearing qualities about Holden. He is this cynical teen, full of angst, and full of distrust of adults, yet his dream of what he could become is full of hope and promise.
Despite all his skepticism (which he retreats to throughout the book), Holden wants to save the children of the world (from falling off the cliff). The cliff, at least in Holden's mind, could be a metaphor for "falling into adult phoniness" or it could be more general than that. Perhaps Holden wants to save them from all dangerous things. It is an inspired, simplistic, hopeful, and naive aspiration from a teen struggling to find a genuine identity. Among other things, the novel is about Holden trying to find a way to be an adult without being phony. Becoming the catcher in the rye is a way for him to envision this.