Whatever a school happens to call it in the application form, it is best thought of as an intellectual statement of preparation / purpose: What are the things that equip you to do well in the grad school and beyond, and how does what you propose to do fit cohesively with or build upon what you’ve done before? All of this is different than a statement that is all about why grad school would fulfill your dreams (you might think about employing the “how are you a better prepared candidate than my neighbor who also loves to read literature” test to various aspects of your narrative statement).

I should say first that my advice about these essays for grad school tends to be on the conservative side, designed to help students minimize taking risks that may backfire. There are so many of these application essays for a graduate admissions person or committee to read that the reasons to put people in the rejection pile sometimes are often more central in the readers’ minds; also, with this many statements to read, consider the possibility that these people are also potentially grumpy and tired, such that whimsy, irony, self-deprecation, etc. might not achieve the desired result. So you want to write defensively with this in mind, in a sense. I think that most people tend to give out this kind of conservative advice, as the competition for grad school slots, particularly ph.d. programs, gets increasingly competitive and the stack of applications in which yours will appear grows higher and higher.

1. Do not spend a lot of time praising the department—you can and should mention particular strengths the department offers (multiple faculty publishing and/or teaching in particular areas that fit with your experience/interests)  as a claim about your fit with the department, so that any praise serves a purpose. But don’t go on about how great they are: this takes space away from details/claims about your preparedness, and it can look sketchy. It's also potentially tricky to mention particular faculty members with whom you'd like to work. Sometimes this is fine in the humanities, although sometimes faculty urge against it (what if the faculty member you are interested in is about to go on leave? or there is bad blood between admissions committee readers and that faculty member? or that faculty member isn’t taking on new graduate students at the moment? etc.).
2. The beginning of the statement:
   
   The admissions director or committee reader is looking to read efficiently. So the safest course is to open with an intro and thesis more like a traditional academic essay that is also skim-proof. Briefly assert your goals and mention your qualifications that make you a strong candidate for this particular or particular kind of grad program.

3. Order of the body: 

   You do want to tell a story about yourself to narrate your intellectual discovery process, your growth in terms of original research, and your ability to work well independently (all things that  the work of grad school requires and are crucial at the PhD level). Orienting the entire body of the essay chronologically around a narrative of development means, unfortunately, that the most recent, and perhaps most remarkable things about your preparation, evidence of skills helpful for grad school, etc. will come way too late in the essay.

   So my advice is to either use a reverse chronology approach, or start with the most recent/impressive things about you and then back up into an earlier point of origin such that you can allow your arc of development to unfold from there to return us to the present.  Either way, you're hitting the reader with your biggest impact assets early on in the statement, so that you are making a strong impression out of the gate (and along the way ensuring your reader is reading your whole statement carefully).

4. Also try to employ, again with a reader in mind who might be tempted to read quickly, a topic sentence model for your body paragraphs in which you make claims about the particular skill or content relevant to your proposed graduate study that X or Y experiences have given you. In that vein, you can elaborate on individual projects you've worked on or the content of particular classes, etc. If you're not wedded to the chronological model as I suggest above, then you're free to dip in and out of relevant projects/experiences that speak to a set of skills or knowledge base when you need to, no matter when they occurred in your academic life.  And you might be freer to elaborate on the things most important (sometimes this is hard to do in a chronology essay, since it can be tempting to want all the events on the timeline to wear even levels of detail).

5. Finally, I always suggest that writers share a draft with at least a few different readers: A. faculty, particularly those who have experience on a graduate admissions committee; B. faculty recommenders writing for you, and/or those who have worked with you closely. This can also help recommenders to flesh out their own letters  for you (maybe A and B are the same, which is great), C. people who know you really well and have known you a long time (in case you forget to mention things about yourself that are impressive and/or relevant).

   You have so little control over the conditions under which your essay will be read by an admissions director/committee member, so you want to test drive your essay with a few different people who can bring different things to their reading.

-- Rebecca Walsh