The climax of To Kill a Mockingbird is the ending of the trial, when Tom Robinson is convicted.
The climax of the book is the turning point, and the point where things are different. For the characters, most of the book revolves around the trial. When the trial is over, most of the conflicts are over with it, because most of them revolved around Atticus defending Tom Robinson.
When Tom Robinson is convicted, it is a sad ending for the Finch family. Atticus lost, and Jem saw the dark side of Maycomb.
It was Jem's turn to cry. His face was streaked with angry tears as we made our way through the cheerful crowd. "It ain't right," he muttered, all the way to the corner of the square where we found Atticus waiting. (ch 22)
Jem expected more of Maycomb and its people. He was surprised that they could hear the same testimony he did, and still convict a man that was obviously innocent. Scout does not understand why Jem is so upset, so she has to face it too. It is just part of growing up the process of getting older for both of them.