Everyone is unique but some are more unique than others. Is that the contrapositive of Animal Farm? I always like a quesion in uniform, but not as much as I like a man in one. I am so bleary-eyed from these applications right now that I think I'm a little crazy.
I think the quote was "Everyone is equal, but some are more equal than others," unless I don't remember it correctly.
Anyway, a diversity statement is for one to explain diversity-related things, ie growing up in a housing project in the slums of Detroit, being a URM, being GBLT, being born in KLDJFKLDSJDS-istan to parents that were both doing Peace Corps and raised you there until you were old enough for college (and you attended highschool with the kids there or your parents homeschooled you or something, and you somehow managed to take the SATs and get into college, and you got a full scholarship), which was the first time you ever came to America and now you want to help the third world country through legal advocacy or something like that, or if you were a child actor or are currently a celeb or are married to one, et cetera.
Depending on how their application is worded, it might not necessarily mean disadvantaged or unique per se. Sometimes it could just be an opportunity for an upper middle class white kid to talk about where he/she grew up; but if you have doubts, your pre-law advisor might be able to help you out more than we could.