Essays are used to learn more about your reasons for applying to the course, university or company and your ability to benefit from and contribute to it. Your answers will let you state your case more fully than other sections of the application, and provide the evaluator with better insight about you and how you differ from the other applicants. In marginal cases, the essays are used to decide whether an applicant will be selected. The purpose of the admissions essay is to convey a sense of your unique character to the admissions committee. The essay also demonstrates your writing skills as well as your ability to organize your thoughts coherently.
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.