Kathmandu2013,
First off, congratulations on waging and winning your battle -- that's a truly wonderful.
Speaking more generally, I believe that the focus of these sorts of questions is on the last part of the prompt: What did you learn? As was mentioned above, the AdComs are trying to figure out who you are as a person, so they're really interested in what you put into/took out of your challenge. This speaks to your character and what sort of wherewithal you have, two very important data points for them.
To that end, personal or professional stories work equally for this type of piece. What I would encourage is that you (and all applicants) is to find a balance between using stories from all areas of your life. Applications that focus entirely on work tend to leave out very important parts of personalities -- and, obviously, applications that miss any sort of reference to work tend to fall flat.
Hope this is helpful. If you'd like to speak more, please feel free to utilize the link below to schedule a free consultation.
Best,
MBA Prep School