Read the questions that you are supposed to answer on the school's application form. Many schools have a fairly open question for your admissions goal statement, such as "Why do you want to go to our school?" Others may ask for a specific focus to the statement, such as asking how you plan to use your education for your career or what you plan to study at the school.
Research the school and note specifics about why you wish to attend that school. For example, you may want to work with a particular professor in the program or your intended research may require the use of stem cells, which only a few universities use.
Determine what might set you apart from the other candidates. For example, you may have real-world experience and skills that can contribute to the program or an experience in your life that led you to this field of study. Stating that you've "always been good at math" won't get you into a graduate program at MIT because that statement is true of all applicants. You need to tell the school what makes you distinctive.
Explain how the program will help you reach your career goals. This might include future plans for research, an idea for your own business or anything else career-related.
Include specifics about what skills and knowledge you would bring to the school. You might, for example, have experience conducting experiments that are similar to the research within the program or you may have been published in an area that compliments the current department's areas of studies.
Pull all of this information together in an essay that answers the question the university asked. Always be as specific as possible about your talents.
Wait a day and go back to edit your piece. The break will mean that your mind is refreshed.