Every school has a guy who is so obnoxious and annoying that you have no idea how he has any friends. But he does. Kevin Stillman is that guy. He's rude, crude, and socially unacceptable. About the new girl, he says, "She's new, she's blue, she needs a screw" (3.24). Actually, the bigger crime here is that he isn't funny, but he thinks he is.
Conrad reaches a breakthrough when he breaks through Stillman's face. Tired of Stillman's wisecracks, "something explodes inside [Conrad's] head" (22.31), and he punches Stillman in the nose.
In classic bully fashion, we never see Stillman again.
Within the context of the book, the fight is a good thing, because Conrad is letting out his anger. He's kept his emotions bottled up for so long that it's good for him to get them out, even in this way. Still, we're just gonna say that if you're feeling the same way, maybe you should take up kickboxing or something before you go around breaking noses.