Why is it important to breath through your nose and out through your mouth when you exercise?

Breathing in this manner helps you to breathe into your diaphragm, instead of just the upper part of the lungs, which is what mose people tend to do. Proper breathing should be deep breaths into the diaphragm and into the lowest part of the lung, thereby filling them up as much as possible.

One way to tell if you're breathing properly is your gut - when breathing deep into the lungs, you'll feel like it's actually filling up the lower part of your gut when you do so. The incorrect way will feel like you're breathing shallow, and you'll get out of breath faster when you exercise.