I have no idea what they are looking for
First of all, I think it's wonderful that you're taking on the challenge of a piano competition. If you've never been in a competition before, you'll never forget the experience! For most regional competitions, to become accepted, all you really need to display is technique. However, to place in the top tier, the pianist needs more than technical mastery, one has to be versatile in various genres of music. So to answer your question, at the end, judges are looking for that "exceptional musician" whose interpretation stands out above the other contestants. We all know it, when we hear it - it's that musical "WOW" factor!
How do you get "Wow" in front of your name?... It's in your character, but it can be developed over time. Everyone experiences life differently. Besides innate talent, that musical "Wow" factor is earned through knowledge, reading, history, aesthetics, culture, personal identity, morality, psychology, experiencing life, work, taking risks, thinking outside the box - creative spirit & vision, balance exaggeration/inhibition, humor, suffering, humility, elation, time, spirituality/faith, and what I call "vicarious transformation" - the ability to place yourself in the composer's mental state when you're on stage. Give yourself all the time to prepare yourself when you're up there. You have to be a demon and angel at the same time - Life is full of contrasts. Don't be afraid to communicate! It's a quality that the greatest pianists possess.
It's been a while... I was 16 when I had my last piano competition. (during a period in my life that I could practice:) Whatever happens, don't take it personally. I always think it's better to try and fail, rather than to prove that it can't be done. You have to go with the attitude that you have absolutely nothing to lose. You've taken an admirable first step in getting the courage to apply. That alone deserves congratulations! BRAVO!