I had a Grad Asst reading/rating applications for two years and also sat on the ADCOM of my med school. While I can give you my perspective, keep in mind that I have NO IDEA how other schools do things. Anyway, our admission director screened people based upon GPA, MCATs and who knows what else. Those that passed this step got secondaries with additional essays. I, along with a few others, would then read all the essays and rate them (blinded to GPA/MCAT). We were looking for applicants that fit our program's mission and who seemed like they'd work and get along well with the other med students. You didn't have to be a perfect fit across the board. It was a gestalt. We rated the application in various categories and also had room to write about the applicant's strengths and weaknesses.
I'd say 80% of all AMCAS applications I read were essentially the same (I've always wanted to be a doctor because.... In college I did the following activities to ensure a well balanced lifestyle.... I volunteered/worked in medical environment X and enjoyed the mental challenge and saw the importance of being compassionate.... You get the picture). 10% of the applications were plain bad fits for our program, had sloppy applications, or just struck me wrong for one reason or another (arrogance, naivete, etc.). The other 10% had AMAZING stories of how they came to be where they were. Even in retrospect, I never could have written an essay that fell into this category because my life was more typical like the majority of applicants.
So, what do you do if you don't have an amazing story? What I found helped differentiate the typical 80% essays came down to one general principal. In the better essays, the applicant didn't have to say I'm X (where X = compassionate, dedicated, mature, intelligent, motivated, a leader, a person with inner strength, integrity, a sense of humor, ...) because they told a story that made those characteristics clear and allowed the reader to reach those conclusions. Weaker applications would have sentences like "I'm a caring person with strong values and a drive to became a great physician" without giving examples, leaving the reader left only with the applicant's opinion of his/herself. All the rambling aside, I'd advise the following: think of 3 characteristics you'd want the reader to write down about you after reading the essay. Then write an essay in some story like fashion without using those words (no cheating by using synonyms!). Have friends/family read it afterwards and ask them to tell you what characteristics the essay communicated. Ultimately, you can use the words you want but the essay should basically communicate those attributes without you having to state it bluntly.
Hope this helps.