Diaphragmatic breathing

Diaphragmatic breathing, or deep breathing, is breathing that is done by contracting the diaphragm, a muscle located horizontally between the thoracic cavity and abdominal cavity. Air enters the lungs as the diaphragm strongly contracts, but unlike during traditional relaxed breathing ("eupnea") the intercostal muscles of the chest do minimal work in this process. The belly also expands during this type of breathing to make room for the contraction of the diaphragm. 
Explanation.
According to the National Center for Complementary and Integrative Health, "12.7 percent of American adults [have] used deep-breathing exercises... for health purposes," which it describes as follows, "Deep breathing involves slow and deep inhalation through the nose, usually to a count of 10, followed by slow and complete exhalation for a similar count. The process may be repeated 5 to 10 times, several times a day."
According to the University of Texas Counseling and Mental Health Center, "Diaphragmatic breathing allows one to take normal breaths while maximizing the amount of oxygen that goes into the bloodstream. It is a way of interrupting the 'Fight or Flight' response and triggering the body's normal relaxation response." They provide a video demonstration.
Diaphragmatic breathing has a physiological effect on the body by assisting in blood flow, lowering pulse rate and blood pressure "by improving vagal activity and reducing the sympathetic reaction." 
In complementary and alternative medicine.
Some practitioners of complementary and alternative medicine believe that particular kinds of breathing they identify as diaphragm breathing can be used to bring about health benefits.
Deep breathing exercises are sometimes used as a form of relaxation, that, when practiced regularly, may lead to the relief or prevention of symptoms commonly associated with stress, which may include high blood pressure, headaches, stomach conditions, depression, anxiety, and others.
Due to the lung expansion being lower (inferior) on the body as opposed to higher up (superior), it is referred to as 'deep' and the higher lung expansion of rib cage breathing is referred to as 'shallow'. The actual volume of air taken into the lungs with either means varies.
Relation to yoga and meditation.
Hatha Yoga, tai chi and meditation traditions draw a clear distinction between diaphragmatic breathing and abdominal breathing or belly breathing. The more specific technique of diaphragmatic breathing is said to be more beneficial.
Fitness and Wellness.
This deep breathing technique has an effect on the physiology of stress, a process that can be detrimental to a "person's physical and/or mental health". Stress can increase the secretion of cortisol which leads to a domino effect of increasing respiratory rate, heart rate and systolic blood pressure. Diaphragmatic breathing helps decrease the cortisol levels through its technique of expanding the lungs into the diaphragm in order to decrease respiratory rate by developing a pattern of inhalation and exhalation. According to WHO, there is an increasing cost of psychosocial counselling and medication to aid in the treatment of stress but researchers have found that diaphragmatic breathing could provide a cost-efficient and accessible way of helping those combat high stress. 
There is also evidence that diaphragmatic breathing has an effect in managing and reducing symptoms of irritable bowel syndrome (IBS), a chronic condition with symptoms of "abdominal cramping, discomfort or pain, bloating, loose or frequent stools and constipation, and can significantly reduce the quality of life." This breathing technique helps increase a balance in the sympathetic and parasympathetic systems. A case study on a patient with IBS has shown that it helps relieve discomfort of the bowel through the increasing blood flow that enters the abdomen thus warming it to relax the body and relieve pain in the stomach. 
Benefits.
The use of diaphragmatic breathing is commonly practiced, especially in those patients with chronic obstructive pulmonary disease, to improve a variety of factors such as pulmonary function, cardiorespiratory fitness, respiratory muscle length, and respiratory muscle strength. Specifically, diaphragmatic breathing exercise is essential to asthmatics since breathing in these patients is of the thoracic type in association with decreased chest expansion and chest deformity as a result of a deformed sternum like pectus excavatum (funnel chest); a shortened diaphragm, intercostals and accessory muscles from prolonged spasm causing stenosis of the major airways leading to an abnormal respiratory pattern.
Relation to music.
Diaphragmatic breathing is also widely considered essential for best possible singing performance. Diaphragmatic breathing also allows wind instrumentalists to maximise intake of air, minimising the number of breaths required for progressing players.