No, the word frindle is not a real word. In the story, however, it becomes a real word. The genre of the book is realistic fiction, and in the story the word frindle winds up in the dictionary.
The main character, Nick, asks his teacher one day who invents words and how they end up in the dictionary. "'Who says dog means dog?'" he asks. His teacher asks him to research it, which he does.
Nick decides that he should invent a new word. He decides to call a pen a "frindle." He and his friends start calling pens "frindles" in class and at school. This causes trouble, especially with his teacher, Mrs. Granger.
A phenomenon began. Soon everyone was talking about frindles. Nick appeared in the newspaper, on television, and on the radio to tell about his new word. Merchandise was sold. Nick became rich. Eventually, frindle became a word in the dictionary.