EDIT: U2's response was submitted while I was writing this. After reading it, my inclination is to delete mine. What the heck, I'll leave it here. But I think she's more on track with what they're probably looking for.
In what section of the application does the question appear? Do you think it's along the lines of special needs, allergies, medications, or unusual care requirements? Or is it more along the lines of, "tell us what makes your child a good match for our program?"
If it's the former, it should be fairly straight forward. You children either have special needs or they don't.
Is this school very competitive to get into? If so, it's more likely the question is asking you to explain why your child should be selected over the other applicants.
I must preface by saying I don't have any kids, don't run a kindergarten, and am most assuredly not an expert on this topic. (
notice it doesn't stop me from offering an opinion, though.) In my job, I do read a lot of resumes and conduct interviews. I'm not sure how that translates to filling out a kindergarten application -- probably not at all -- but here's what I'd do if it were my child and I were filling it out.
Mention that your children are excited at the prospect of starting school.
Discuss any special aptitudes you've noticed with your child (e.g., "Johnny has displayed a love for learning. He has already mastered the alphabet and is able to recognize many words.") Also talk about some of the things your children particularly like to do (e.g., "Johnny is a big fan of music. He loves to sing and has expressed interest in learning to play the piano.")
Also likening this to a job resume, try to focus on why your children would be assets to the school, rather than on how the school will benefit them. That's a tough one, but if you think about it I bet you can come up with some.
How are they in social settings? (e.g., "Johnny is a very social child. At the playground, he prefers to play with other children rather than on his own.")
Tout the fact that they're well behaved, have amiable personalities, are eager to learn and try new things, and have an overall upbeat and happy disposition. (They do, don't they?)
Have they had favorable experiences in other classroom settings? If so, definitely mention it. (e.g., "Johnny is very comfortable in a classroom environment. His Sunday school teacher frequently tells us how well behaved and participatory he is.")
