This meeting sets off the action in the rest of the novel, and the relationship between the two profoundly affects the narrator's life. It's also through the narrator's eyes that we get to know Holly, so it's pretty important that the two become acquainted.
The narrator realizes that he and Holly are on totally different wavelengths. She criticizes the things he writes about (and completely misunderstands them), and he just doesn't get the choices she makes. After the narrator insults her intelligence and wants to hit her, Holly throws him out of her apartment. The narrator vows never to talk to her again.
The narrator is still angry with Holly, but he notices a strange man watching her apartment and feels compelled to warn her about him. We learn that this man is Holly's husband and that she married him when she was just fourteen years old. He relates the sad story of her childhood and this complicates the narrator's perception of Holly (and ours, too).
There are quite a few climactic moments in the novel, but this one is pretty big since it represents the big break between Holly and the narrator and Holly and New York (the city she loves). Once she has decided to leave, the narrator is forced to think about what his life will be like without her, and he also admits that he's a little in love with Holly. Everything changes from this point on, which is why we think it's the climax of the story.
Holly's arrest totally interrupts her plans and we're left in major suspense about her fate. Will she go to jail? Will she make it to Brazil? Will she admit to knowing about what Sally was really up to? We don't know what's going to happen to her, and this is the first time in the novel that Holly seems like she's in a situation she won't be able to charm her way out of.
Now that Holly knows she's not going to live happily ever after with José and their baby, she starts to make some definite decisions about her future (sort of). She prepares to skip town, to leave behind the narrator and Joe Bell and the mess with Sally Tomato, and she starts to wind down her time in New York City (while finally admitting that she's scared of continuing her life as it has been). This would seem like the conclusion, yet there's still more to come.
The conclusion is pretty open-ended, so we can't really say for sure what happens to Holly once and for all. But she does leave New York and we do know that she has made it to South America, so in terms of the actual plot, this signifies the end of the story's action. The postcard lets us know that she's no longer living in the brownstone, no longer hanging out with the narrator, and no longer socializing in the same circles.