After somewhere between three and five hours, your body stops processing its last meal. There's nothing left to absorb, so insulin levels naturally decrease. Then, somewhere between eight and 12 hours after that last meal, your body starts burning stored fat. (Why don't you start burning fat sooner? Biology is sometimes a pain in the ass; it's like our bodies will do anything to hang on to fat.)
In a way, moderate-intensity physical activity is that "magic pill" a lot of people are looking for, because the health benefits go beyond keeping your waistline trim: Not only can it reduce your risk of cancer, stroke, diabetes and heart attacks, but studies have shown that physical activity can significantly improve the moods of patients with major depressive disorders.