What I learned about breathing this way in tai chi, and also by using this method in running, is that you better oxygenate your blood, therefore generate more energy.
I teach my runners to breathe into their bellies so that they can experience the difference from breathing shallowly into their chests. Inhale, count to 2, exhale, count to 3 - it's amazing how controlled your running pace will feel, and more effortless.
Practicing breathing will also improve your posture, as you will be forced into posture correction in order to breathe properly. That's a nice benefit.