This deep breathing is marked by expansion of the stomach (abdomen) rather than the chest when breathing. It is generally considered a healthier and fuller way to ingest oxygen, and is often used as a therapy for hyperventilation and anxiety disorders.
Note that some yoga 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.
Though the diaphragm is the primary breathing muscle, it is believed that many people have little sensory awareness of their diaphragm and almost no idea of how to engage it more fully or even of how it works. There are some breath therapists and breathing teachers who believe that because of the increasing stress of modern life and the resulting over-stimulation of the sympathetic nervous system, as well as of the ideal of the hard, flat belly, that many people carry excessive tension in the belly, chest, and back, and this tension makes it difficult for the diaphragm to move freely through its full range of motion.
To breathe diaphragmatically, or with the diaphragm, one must draw air into the lungs in a way which will expand the stomach and not the chest. It is best to perform these breaths as long, slow intakes of air - allowing the body to absorb all of the inhaled oxygen while simultaneously relaxing the breather.
To do this comfortably, it is often best to loosen tight-fitting pants/belts/skirts as these can interfere with the body's ability to intake air. While at first one may not feel comfortable not expanding the chest during breathing, diaphragmatic breathing actually fills up the majority of the lungs with oxygen, much more than chest-breathing or shallow breathing.
Many yoga and pranayama teachers believe that the most complete and fullest way of breathing is the "three-part breath," also called in yoga "The Complete Breath," which includes diaphragmatic breathing as the first step, followed by thorax expansion and then chest expansion. This way of breathing is known in Tantric yoga as that which facilitates the greatest flow of life force through the body. There are several variations of the "three-part breath," but many breath therapists and breathing teachers maintain that this approach can create breathing imbalances and other problems.
During stress and anger, we tend to inhale and hold our breath. The most significant, therapeutic aspect of this breathing is the exhalation---which is at least two times the length of the inhalation. The exhalation alerts the body that it can relax and resume essential body functions and not remain in a state of fight or flight.