The university want to avoid a situation where they take on a student who fails to complete - look at your application from their point of view. They want to know that you will be competent and happy enough to survive four arduous years at their institution, with the loneliness and destitution that is the life of a graduate student. Give them the signals that show them that you will survive.
Your statement of purposes is an opportunity to show that you have the diligence, foresight and skill to check the research strengths of their school, and you have some sensible reason for regarding that school as a preference for you. The university will want to know that your interests are broad enough to allow you to find a suitable research topic that can be supervised by someone in their faculty (preferably with backup, in case they have staff changes during your candidature), and you are able to narrow your focus when needed to get down dirty and do the work. They want to know that you have interest backed up by competence and diligence.
Demonstrate some knowledge of the faculty and their research interests/projects: This is an opportunity to demonstrate that you have done your due diligence and checked the various school webpages, faculty profiles, etc., to show that you are aware of the broad research strengths of the school, what they are best known for, and how reputable their research is in different fields. If you have read some of the papers by their faculty, mention this. If you have seen some of the faculty give talks, presentations, etc., in an area of interest to you, mention this. Show that you have a broad awareness of the main strengths of the school. If it is a prestigious school, their strengths are probably numerous, but you should still be able to mention a few specific areas.
Mention some areas of interest to you that align with the school: It is important to be able to mention at least a few research areas of interest to you, and be able to point to faculty/research groups in the school that work in those areas. Bonus points for being able to point to some specific work by the faculty that you particularly liked and is of interest to you (bearing in mind that you are only just applying for grad school, so you probably don't have a wide knowledge of the literature in any area). Show that when you have learned about various fields in your undergraduate degree, it gave you lots of ideas for possible avenues of research. Ideally you will have lots of ideas -your mind is flooded with them- and you can't wait to talk to the professors at this school to see if any of your ideas are feasible!
Back up your interests with your skills/qualifications: If you're interested in a particular field of study done by this school, what evidence can you show to demonstrate that you are well-qualified to start study in that area. Did you do well studying this area as an undergraduate? Did you get good grades, win an award, write a good project, etc.? Did you ever do any research work on it as an undergraduate? (Remember that most of the applicants to a prestigious grad program probably nailed their undergraduate degree, so make your achievements relative to this cohort.) Ideally you want your statement of purpose to show interest backed up by evidence of high competence (relative to other applicants).
Show how excited you are to study there: Convince the school that you will be happy there, and you have the personal skills to make friends and create a life for yourself that will sustain your time there. Unhappiness/loneliness is a killer of graduate degrees, so they want to know that you are a low-risk candidate for dropping out. You should have a tone of excited anticipation - show that you are looking forward to graduate school, and you are excited about studying there.