Stress is as much a physical response as it is an emotional one. When we're "stressed out" the blood leaves our extremities and flows to our heart and lungs where it perceives the body will need it most (in preparation for action). This dates back to the primordial fight or flight response.
When stress occurs, the body also releases the cortisol hormone which can negatively affect your health. Heightened cortisol levels can lead to glucose imbalances, improper brain functioning, hypertension, thyroidism and weight gain (to name a few). Eventually taking its toll on the heart, respiratory, immune, nervous system and much more.
So you see, it really does pay to breathe your way through traffic, or that rude counter clerk in the check out line. It's not only about being zen for zen sake, it's about arriving at a state of greater peace, so we can live free from the physical toll that stress inevitably inflicts on every aspect of our body.