“When the breath wanders, the mind is unsteady, but when the breath is still, so is the mind still.”
– Hatha Yoga Pradeepika||

Breath is life. we can live for  days  without food or water, but deprive us of breath and we die in minutes. In view of this, it is astonishing how little attention we pay in normal life to the importance of breathing correctly.  To a yogi there are two main functions of proper breathing: to bring more oxygen to the blood and thus to the brain; and to control vital prana or vital energy, leading to control of mind. Pranayama- the science of breath control – consists of a series of exercises, especially intended to meet these needs and keep the body in vibrant health.
There are three basic types of breathing – calvicular (shallow), intercostals (middle) and abdominal breathing (deep). A full yogik breath combines all three, beginning with a deep breath and continuing the inhalation through the intercostals and calvicular areas. 
Most people have forgotten how to breathe properly. They breathe shallowly, through the mouth, and make little or no use of the diaphragm – either lifting the shoulders or contracting the abdomen while they inhale. In this way, a small amount of oxygen is taken in and only the top of the lungs used, resulting in lack of vitality and a low resistance to disease.
The practice of yoga demands that you reverse these habits. Breathing correctly means breathing through the nose, keeping the mouth closed, and involves a full inhalation and exhalation which brings the whole of your lungs to play. When you exhale, the abdomen contracts and the diaphragm moves up, massaging the heart; when you inhale, the abdomen expands and the diaphragm moves down, massaging the abdominal organs.
Just as there are three stages for an asana, so in Pranayama there are three parts to each breath – inhalation, retention, and exhalation. People often think of inhalation as the most essential stage of breathing but in fact it is exhalation that holds the key. For the more stale air you exhale, the more fresh you can inhale. The yogik breathing exercises lay special emphasis on a prolonged retention and exhalation – indeed in some exercises the out breath is twice as long as the in breath, and the retention four times as long.
When you inhale through your nose, the air is warmed and filtered. But from the yogik point of view the overriding reason for breathing nasally is prana. Just as you need to inhale through the nose to extract scents from the air, so you must inhale nasally to maximize the amount of prana taken in – for at the back of the nose lie the olfactory organs through which prana passes to reach the central nervous system and brain.

Rhythmic, deep and slow respiration stimulates and is stimulated by calm, content, states of mind. Irregular  breathing disrupts the rhythms of the brain and leads to physical, emotional and mental blocks. These, in turn, lead to inner conflict, an unbalanced personality, a disordered lifestyle and disease. Pranayama establishes regular breathing patterns, breaking this negative cycle and reversing the debilitating process. It does so by giving us control of the breath and re-establishing the natural, relaxed rhythms of the body and mind. 
The yoga breathing exercises teach you how to control prana and thus to control the mind, for the two are independent. When you are angry or scared, your breathing is shallow, rapid and irregular; conversely, when you are relaxed or deep in thought, your breathing becomes slow. You can easily test this yourself. Listen for a moment to the lowest sound in the room.