Simply put , our muscles needs more oxygen ( which explains why we breathe fast after an excercise ) . How is that related to the heart rate though? Because as we breathe more frequently , that means that we DO get in enough oxygen but it's still not transported to the muscles in need . I think you know that the circulatory system transports oxygen throughout your whole body . So since there's an increased amount of oxygen in your lungs , your heart will pump faster to transport the increasing oxygen amount as fast as possible ( which explains why our heart rates increase when we breathe more after an excercise)