What is optimal breathing? It is much more than just standing around and sucking air in and pushing it out. In my research regarding breathing, western medicine has little to offer about breathing as a solution to health problems. However, it seems that all the knowledge and research comes out of Europe and through the yogis of India.
Leon Chaitow, an osteopath/naturopath based in London, is one of my favorite authors on the subject of breathing. In his book Recognizing and Treating Breathing Disorders, on Pg 26 is a description of optimal breathing:

Optimal breathing involves:

• Since the objective of breathing is to meet the metabolic demands of the body, oxygen (O 2 ) and carbon dioxide (CO 2 ) need to be efficiently moved into and out of the lungs ( Abernethy et al 1996 ).
• During quiet breathing, respiratory efficiency is achieved as the diaphragm descends into the abdominal cavity during inhalation, increasing the vertical dimensions of the thorax as the ribs rise and move laterally, to expand the transverse dimensions of the thorax.
• The diaphragm relaxing, and returning to its domed position on exhalation follows this sequence, as the abdomen and chest wall return to their starting positions.
• In good health, meeting the metabolic demands of the body optimally requires a steady, rhythmical pattern with a respiratory rate of 10-14 breaths per minute; involving a ratio of inspiration to expiration of 1 : 1.5-2.
• Ideally the least amount of mechanical effort from the respiratory musculature should be involved ( Jones et al 2003 ).
• If such an optimal pattern is disrupted, abnormal and potentially inefficient respiratory mechanics may become the new norm – with the emergence of a breathing pattern disorder.

There are actually four ways to breathe according to the yogis of India. In Light on Pranayama by B. K. S. Iyengar, on pg. 21:

Respiration may be classified into four types:
(a) High or clavicular breathing, where the relevant muscles in the neck mainly activate the top parts of the lungs.
(b) Intercostal or midbreathing, where only the central parts of lungs are activated.
(c) Low or diaphragmatic breathing, where the lower portions of the lungs are activated chiefly, while the top and central portions remain less active.
(d) In total or pranayamic breathing, the entire lungs are used to their fullest capacity.

You’d think that we all knew how to breathe correctly since we do it all day long. However, it seems that over time, we have developed a ton of faulty breathing patterns. In Karl Lewit’s Manipulative Therapy, pg. 31:

The most important faulty respiratory stereotype, seen from the point of view of the locomotor system, is that in which the thorax is lifted during inhalation ( Parow 1954 ). In this pattern the thorax is lifted in the cranial direction by the scalene and sternocleidomastoid muscles and the superior fixator muscles of the shoulder girdle, but without expansion of the chest.
Termed ‘clavicular breathing,’ it involves a reversal of the normal respiratory mechanism, since the scalene muscles, which normally only fix the thorax, raise the lung; resistance is offered by the diaphragm. This is inefficient, not only from the respiratory point of view, in that the volume of the chest increases very little, but also for the locomotor system, because of the chronic overload that this causes to the cervical spine.
A further effect is that fixation of the thorax to the pelvis no longer occurs, causing instability of the lumbar spine. The pattern of lifting the thorax during inhalation, or clavicular breathing, can be asymmetric, if one shoulder is raised more than the other. The stress on the cervical spine is then greater on this side. Clavicular breathing is the disturbance that typically occurs when sitting but not maintaining a straight posture, because this makes expansion of the thorax difficult.

and then on pg. 156, what can happen if you exhibit faulty breathing patterns:

Lifting the thorax during inhalation (clavicular breathing)

Tension	Superior parts of abdominal muscles, pectoralis, scalene, diaphragm, sternocleidomastoid muscles, short craniocervical extensors, levator scapulae, superior part of trapezius
Painful points of attachment	Posterior arch and transverse processes of atlas, spinous process of C2, nuchal line, sternal end of clavicle, superior border of scapula, sternocostal joints and upper ribs
Joint dysfunction (restrictions)	Atlanto- occipital and atlanto- axial joints, cervicothoracic junction, upper ribs, thoracic spine

Many things can cause these poor breathing patterns to establish themselves: physical (ie. injury) and emotional (ie. fear, stress) – even intellectual (ie. watching others breathe as models for their own breathing). Over the decades of life, all of these add up to developing poor patterns, certainly poor for performance much less quality of life. So it is important to get back to activating the diaphragm for breathing, where we can get to optimal breathing (as described previously).
Activating the diaphragm has function beyond just that of breathing. For performance, the diaphragm is critical in proper stabilization of the torso. As stated in Manipulative Therapy pg. 30, “The diaphragm is a respiratory muscle with a postural function, and the abdominal muscles are postural muscles with a respiratory function.” Maintaining proper posture and retaining that shape during movement is VERY HARD without the diaphragm helping.
From Recognizing and Treating Breathing Disorders, pg. 17:

A number of studies document coordinated synergy of the diaphragm, transverse abdominis, pelvic floor and the multifidus muscles during postural activity ( Hodges & Gandevia 2000b ). However, this synergy is not under full volitional control and modifiable. Therefore, the diaphragm, controlled by the CNS, assists in ensuring postural body control. The activity of motor neurons of the phrenic nerve is organized in such a way that the diaphragm simultaneously contributes to respiration as well as body stabilization and other nonventilatory behaviours ( Mantilla & Sieck 2008 ).

How does this stabilization work? From Manipulative Therapy pg. 30-31:

The way this is understood today is as follows: the diaphragm attaches dorsally to the spinal column and laterally to the inferior costal arch, while ventrally the fixed point is provided by the abdominal wall. Here, the co- contraction of the deep layer of the abdominal muscles has a key role. Kolar (2006) showed radiographically that the diaphragm was angled downward in the ventral to dorsal direction if the abdominal muscles were weak. If the abdominal muscles are functioning normally, contraction of the diaphragm during inhalation is accompanied by eccentric contraction of the deep abdominal muscles. This can be clearly palpated laterally above the iliac crest. The effect is not only to enable the diaphragm to function in the most efficient way and, as shown by Kapandji (1974) , to expand the thorax, but also to fix the thorax to the pelvis and so stabilize the lumbar spine. The activation of the abdominal muscles during inhalation was also described by Campbell (1978) and Basmajian (1978) .

Beyond the postural and stabilization function of the diaphragm, it also has other important functions relating to digestion (Recognizing and Treating Breathing Disorders, pg. 20):

During a breathing cycle, a rhythmic compression of the abdominal cavity occurs and leads to a cyclical movement of the internal organs. During inspiration, almost all internal organs of the abdominal and retroperitoneal areas shift several centimetres in a caudal direction ( Xi et al 2009 ). This organ movement and the pressure activity of the diaphragm partially contribute to the transport of food and digestive juices. In this way, the diaphragm assists in digestive processes and significantly contributes to peristalsis and food propulsion.

Removing faulty breathing patterns and re-activating diaphragmatic breathing, thus, has many benefits beyond just getting more air into your body.