Ok, so I know this question is a month+ old, but still a good question.
I'm looking to get a sense of who you are. I'm not interested in "the case that made you realize you loved specialty x" or "the amazing mentor who made you realize you loved specialty x" or "the family member with the disease that was treated by someone in specialty x".
From the rest of the application I get pages and pages of data points which I can put into an excel spreadsheet and assign point values to and churn out a ranked list of applicants. But the PS is an unrankable thing. It gives me insight into the kind of person you are. Unless it's formulaic (which so many of them are) in which case it's a useless piece of paper. It's your chance before an interview to alter your position in the mob, and to be more memorable as the ranking process goes on.