Okay, I'm not applying to NYMC but here is how I would attack this question:
If I were a multi-pierced, anarchist who ate babies but, for some reason wanted to go to medical school - would I tell them about the above? NO! Why not? Because thats not what they want to hear. I'm not saying completely make it up, but what this question is really asking is a two-fold one:
"Why would you make a good doctor"
"What is unique about you"
So think about what characteristics make a good doctor. Responsible, self-less, motivated, enthusiastic, good communicator, scientifically oriented, etc etc etc. How do you exhibit these characteristics? Paint a picture. Don't say I am a caring leader who likes people. Instead give an example of 'what you are like' eg the above might be demonstrated in a particular clinical experience. Be specific.
However, what makes you unique? Imagine everyone is an ideal 'proto-doctor'. What would you add to the class? Do you have the perspective of a URM, economically disadvantaged, strong research, passion for music.
ie in reality I don't think this question is asking anything that much different from most 2ndaries.
You need to show that you have the qualities desirable in a doctor, and that there is something unique or interesting about you.