I have depression, I have starved myself, and I didn't eat for 5 days!! I think you'll be fine for one day!!
Nothing. You'd just be hungry. You can not eat for easily a week without to much effect.
You might lose more fat and gain more muscle, all by skipping a few meals. But even if you don't lose extra fat by fasting, I promise you will lose something important: that ridiculous, unarticulated fear of not eating every few hours.