The climax of a book is the event that all of the earlier tension has led to, the turning point in the story where the action resolves that tension and all of the problems begin to get answered.
In Frindle, by Andrew Clements, the tension revolves around Nick's playful attempt to create a word, "Frindle," which is just another word for "pen." Because words mean what society takes them to mean, as "frindle" becomes more and more widely used in the book, it becomes a more established word. This increases the tension in the story because Nick's teacher, Mrs. Granger, and the school administration fight against the word's growth in order to keep control of their students. Mrs. Granger heads this fight against the word, with her attempts to stomp it out becoming so extreme that local media begins to notice. Of course, this only serves to further publicize "frindle," making it an even more established word.
At one point, Mrs. Granger does a strange thing: She writes a letter, seals it in front of Nick, and tells him to sign it across the back flap to prove it has never been opened.
The climax of the book is the return of this letter. Nick has become wealthy from a trust fund created by his father after he had trademarked the word. Mrs. Granger sends Nick the letter, along with a dictionary that has the word "frindle" in it. The letter tells Nick of how Mrs. Granger had supported him all along, and that she had only fought against the spread of the word to make it grow even quicker.