The climax of a story, also sometimes referred to as the crisis in literary terms, refers to the turning point of the story that informs the reader of the general way the story is going to end. Most of the time, this occurs near the middle to end of the story.
In Charles, the plot action builds throughout the story almost until the very end before the reader realizes the climax and how the story will end. In fact, the author wrote the story with a rather ambiguous ending, allowing the reader to predict the continuing details of how things will work out for the main character, Laurie.
Laurie, who has deceived his parents regarding a fictional character he made up, Charles, spins tales his parents at first believe but then begin to become confused about as the story unfolds. Each day, Laurie returns home speaking of the misbehavior of a fellow kindergarten student, Charles. His parents become more and more concerned about the influence this "Charles" may have on their son until at the end, mom decides to ask to speak with the teacher.
The climax comes with Laurie's mom asks the teacher how she handles all the antics of the ill-behaved Charles. The teacher replies that there is no Charles in their entire kindergarten. The reader is left to conclude that the mother at this point, figures out that Charles is really Laurie.