Not just humor, but the overall tone of your application essay is remarkably important. It's also difficult to get right. When you are asked to write about your accomplishments, those 750 words on how great you are can make you sound like a braggart. Be careful to balance your pride in your achievements with humility and generosity towards others. You also want to avoid sounding like a whiner -- use your essay to show off your skills, not to explain the injustices that lead to your low math score or failure to graduate #1 in your class.
My son wrote the “Grandparent” essay. Well make that the great-grandparent essay. It started with a humorous scene related to the funeral and went on to demonstrate the life-lessons learned from the great-grandparent with a couple of real examples of where my son used those lessons. It was engaging, funny and poignant and a real insight into my son and what he values. It (together with his accomplishments) earned him a likely letter to Harvard and a spot at his first-choice, where he chose to attend. It is not the topic but the delivery.
Longer essays may also contain an introductory page that defines words and phrases of the essay's topic. Most academic institutions require that all substantial facts, quotations, and other porting material in an essay be referenced in a bibliography or works cited page at the end of the text. This scholarly convention helps others (whether teachers or fellow scholars) to understand the basis of facts and quotations the author uses to support the essay's argument and helps readers evaluate to what extent the argument is supported by evidence, and to evaluate the quality of that evidence. The academic essay tests the student's ability to present their thoughts in an organized way and is designed to test their intellectual capabilities.