Your plans for graduate school should naturally lead to a discussion of your fit for a particular program (see below). Think of these topics as paired: First, you need to detail what you plan to study and research; second, you should explain with whom plan to study and research. That second part will vary for each school to which you are applying. Here’s where you need to show that you have specific (but not narrow) interests in your field and they align with the faculty members in the department. 

Again, unlike applying as an undergraduate, you should not survey the university website in general. You’re not applying to the university but to the department or program. As a graduate student, you will take almost all your courses within your department and should consider yourself a student of that one department, not the university itself. Thus, your focus should be on the coursework and faculty in your desired degree program. Professors are easily insulted by applicants who spend too much time writing about opportunities outside their department; no one is impressed by intellectual promiscuity. If you have interdisciplinary interests, explore those once you are enrolled. Your statement of purpose needs to show your fit with the faculty in that particular program. 

Your plans should be specific. Not “I’m interested in 19th-century American history” but this:

from Timothy Burke, “I Choose You, Pikachu”

 “I plan to study American diplomatic history, with an emphasis on the antebellum period. I’m especially interested in how the United States integrated itself into the evolving interstate institutions of the early 19th Century, both before and after the Napoleonic wars.”

Return to your brainstorming and revisit your ideas about what you will do in graduate school. Here’s some advice from an economics professor that applies to all fields:

Professor Sit Nataraj Slavov:

 “In describing your research interests, try to stay away from the hot topics of the day (e.g., the financial crisis). A topic that does not appear to come from news headlines signals a serious, thoughtful, long-term interest in that issue. Your statement should communicate to the committee that you understand what graduate school is all about and that you have carefully thought through your decision to pursue a PhD.”