This section of the novel comes in Chapter Four, and is when we are introduced to Stradlater, who is Holden's roommate at the boarding school that he has just been kicked out of. The conversation that you refer to comes after Stradlater asks Holden to write a descriptive piece of work for him for his English homework whilst he goes out on a date. Stradlater asks him to do it whilst yawning, and then also says that Holden is so good at English that he must not make his descriptive piece "too good," because it will alert the suspicion of their English teacher. He therefore tells Holden to make sure that the commas are not all in the right place. Note how Holden responds:
That's something else that gives me a royal pain. I mean if you're good at writing compositions and somebody starts talking about commas. Stradlater was always doing that. He wanted you to think that the only reason he was lousy at writing compositions was because he stuck all the commas in the wrong place.
Holden is therefore talking about the tendency that we have as humans to pretend that we could be equally as good as other people in a given skill or area if we could be bothered or if we had the time. He backs this up with another example of Ackley talking as if he knew all about basketball and was an expert on it when he wasn't able to play it at all.
Holden has a natural talent for writing. Salinger wishes to establish this fact early in his book for the sake of verisimilitude. The reader must be persuaded that a sixteen-year-old boy who is not even a good student is capable of writing an entire book like The Catcher in the Rye which is full of subtle observations about people and about life. Actually the book is being written by Salinger himself, an older man with many more years of writing experience and life experience. But in various ways, including the little scene with Stradlater, Salinger manages to sustain the illusion that Holden Caulfield is a real person and that he is writing his own story. He doesn't put the commas in the wrong places, but he does use a lot of kid language to characterize himself as a bright and sensitive sixteen-year-old boy.
John Updike's well-known short story "A&P" is told by a nineteen-year-old boy using teenage vernacular. Mark Twain's Huckleberry Finn is probably the prototype for the use of first-person narration in juvenile vernacular, and it is still credible even though Huck Finn is uneducated and must be only semi-literate.