At this moment in the novel, Holden has been musing on the idea of his dead brother, Allie, and thinking not only of Allie but of his death.
As he is writing a descriptive essay for Stradlater about Allie's baseball glove, Holden reflects on his reaction to Allie's death and relates the story of how he broke all the windows in the garage with his fist and broke his hand. The emotional state stirred up by these recollections become attached to Jane Gallagher in a round-about way, leading to a situation where Holden is quite upset.
The chapter opens with a statement to this effect, with the line, "Some things are hard to remember." Having spent time thinking about Allie then thinking about Stradlater and Jane, Holden is in an emotional state where he has trouble controlling himself.
"I could hardly keep my voice from shaking all over the place. Boy, I was getting nervous. I just had a feeling something had gone funny."
As Holden talks with Stradlater, he continues to be upset and gets angry, at one point trying to punch Stradlater in the face.
"It probably would have hurt him a lot, but I did it with my right hand, and I can't make a good fist with that hand. On account of that injury I told you about."
The detail about Holden's fist is an indication that this episode (and Holden's emotional state) is related to Holden's feelings surrounding his dead brother. A good deal of Holden's behavior throughout the novel can be connected to these feelings.
One way to read this scene in the context of the larger novel is to take into account Holden's later claims that all he wants to do with his life is save children from falling off the edge of a cliff. He wants to be the "catcher in the rye," saving children.
Jane belongs to a part of Holden's past where innocence is still intact. He recalls playing checkers with Jane, a fact that Stradlater finds childish. For Holden, Jane might be one of the children that Holden wants to save. What does he want to save her from exactly? That is not entirely clear, but we can infer that Holden wants to save a state of innocence for himself and for others in a way that connects to his brother Allie.
To take an interpretive leap, we might suggest that Holden wants to keep Jane from being corrupted by Stradlater, an athletic high school student who has to shave twice to remove his beard and who is "unscrupulous" according to Holden. Thus Holden's most motivating fears and desires relating to innocence and loss are activated in his confrontation with Stradlater.
Ackley is older than Holden but, to Holden he is "a virgin if I ever saw one." Ackley is, in other words, a rather innocent person. Choosing to take solace in Ackley's room after this fight with Stradlater, Holden is again demonstrating his preferences. He is most comfortable with unsophisticated and childish people (and children).