I'm posting here too an answer I wrote at Quora.
Since motivation is a very personal thing, writing about research interests also is. So, everyone will write in a different way, with no clear-cut and strict rules. Avoid using templates, for example.
But my suggestions are:
1 - Describe your research interests. If your research interests are too broad, they will not tell much about you. If you just tell that you are interested in doing research about Marketing while applying to a Marketing program, for example, it’s just a waste of time. But if you are too specific, it may also be a problem. A research interest that is too specific is also very limited, narrowing opportunities like finding a good advisor for you. If you know a little about research, you can describe that interest in a more academic way, like a research problem.
2 - Tell why you are interested in doing research, and why that subject you described. Telling them “why” will help them to understand your motivations.
3 - If you are interested in something, probably you already know something about it and have some experience to tell. It’s harder to convince someone that you are interested in something if you have never done anything about it. So, write a little about your knowledge and experience.
4 - Why should someone care about your research interests? Doing that kind of research will help your career, the university, companies, countries, the world?
5 - How do you think the program you are applying to can support you in your research interests? A faculty with similar interests? Access to data which are relevant for your interests? Laboratory and equipment?