Highly physical, posture based yoga is extremely popular today. The focus on asana (posture) does sometimes mean that other traditional aspects of yoga are minimized. But mental discipline is as much a part of tyoga as is physical. If there are two archetypal images of yoga they are a person sitting in lotus (a pose of meditation), or a person in an a physically demanding inversion (like head stand). Most practitioners today recognize the importance of both. But unless a teacher is themselves a meditator that part of the practice can be relegated to 5 minutes in Shavasana (laying down) at the end of the class. Shavasana is very helpful. But it is only part of a more nuanced and complex practice. To understand the point of yoga beyond physical movement one needs to look at the interface of mind and body, and something most people know quite intimately: stress.
When all the interdependent systems of the body work in harmony under normal circumstances it is called homeostasis. A stressor is anything that puts a strain on that system. Stressors are a normal part of our environment. It would be bad to have none: stress causes adaptation and growth. And joyful events cause similar effects to difficult ones. But too much stress, or failure to reset to baseline can lead to health problems.
Stress begins with perception of a sensory stimulus. The cognitive part of the brain appraises this stimulus in light of our knowledge and experience. Then we experience an emotional arousal based on this appraisal. That emotional response can be vary in intensity, and be positive or negative. This response moves through the mind/body connection (by way of the hypothalamus) through two pathways: a slower, but longer arousal of the endocrine system, and a faster arousal of the nervous system. The nervous system has two paths: the flight or fight response (sympathetic), and relaxation (parasympathetic). These systems produce a cascade of physical effects designed to let us deal with the situation. Blood flow gets shunted away from food digestion, for example, so the muscles can fight or run. Heart rate goes up, blood pressure goes up, respiration rate increases. If the stressors are not continuous the system can generally return to normal. If the stress becomes chronic, or the body cannot clear the byproducts of arousal homeostasis may reset at a higher level (like gunning your car engine continuously) and the extra wear and tear on the system can lead to a variety of health problems, and general loss of quality of life.
Some stressors are simple: a horn honking loudly behind you, a loud alarm clock going off at your ear. Some are life events: which can be what I call 'big ticket items' (death, divorce, loss of work), and some every day stressors (spilled coffee, bad traffic, eye rolling teenagers). Other stressors have to do with lifestyle choices: a poor diet, a sedentary lifestyle, lack of sleep, loneliness, chronic overwork, work that is too hard or just too heavy a workload. A person's outlook and personality can also become a stressor. That is the glass half empty syndrome. And when stress leads to physical symptoms, those symptoms can cycle back as more stress.
Some stressors can be avoided or controlled. Some can not. We can work on our environment, (e.g. wear ear plugs if our work environment is noisy). We can work on our mental response, (e.g. cognitive therapy is designed to help people shift how they think about things they experience, and one technique to shift emotional response is to use self affirmations, for example). We can work on our physical response. When a common stressor was a wild animal running after you the body's flight or fight response was great. But when your boss puts a huge project in your lap five minutes before you were planning a nice evening sitting by the water climbing a tree or wrestling with him would be counterproductive. However, going for a run, or lifting weights will allow the body to reset its state of physical readiness. There are many other long term strategies for dealing with common modern sources of stress: listing what stresses us and coming up with alternatives, identifying unhealthy lifestyle choices and putting into play methods to change those habits, working on time management, developing social networks, etc.
There are also a wide range of ways to encourage relaxation and reset. When the body is full of the effects of sympathetic arousal it can be useful to work from the body back to the mind. Exercise is great for that. The physical effects of exercise generally counter the effects of sympathetic arousal. Breathing exercises are also useful. Edmund Jacobson wrote about using what he called progressive neuromuscular relaxation. Meditation and visualization are good tools to use, but generally work better (I think) not when 'stress' is high, but as a regular practice, or when the body is calmed down a bit.
Yoga is useful for stress reduction for many reasons. A typical yoga studio is quiet and peaceful. If there is music it is neither loud or cacophonous. The lights are usually not glaring. One removes tight shoes and sits or lies on a mat. If there are snacks they are not rows of highly processed junk. The atmosphere is one of non judgement and self acceptance. People gather together to find health and release and calm.
The physical movement (asana) helps reset the physical effects of stress. The breath work, (pranayama) help reset respiration rate. Breath is autonomic – happens without having to decide to do it – but is also easily willed – can be deepened or slowed by attending to it, making it an ideal place to begin 'destressing'. Selective attention (dharana) through intense focus on alignment and attention to inner tactile (kinesthetic) cues (pratayahara) helps break the cycle of cognitive and emotional focus on stressors. Meditation per se (dhyana) is not always fully engaged within the class, but is always open as an option at the end, when the body is most ready for the experience. And the five or ten minutes of Shavasana at the end allow rest when the body is most open and ready for it, allowing one to leave in a less 'stressed' condition.