Yoga might be considered both a form of exercise and a form of meditation, at once.  The physical postures that are typically thought of as yoga (tree pose, downward-facing dog pose, bridge pose...) all stretch, strengthen and bring balance to the body.  The potential physical benefits of doing these postures are many, and this is why people come to their second class.  However, at least an equally important reason that people come to their third class, and then their fourth and tenth and hundredth, is that practicing yoga also calms the mind.  Since this calming of those persistent fluctuations of the mind happens in conjunction with the new practitioner standing taller, breathing fully into a more expanded chest, having more balance, and generally feeling both stronger and more at ease in his or her body, it's no wonder that this ancient form of self study is so popular.    

Intelligent practice of the postures, or asanas, makes these physical and mental benefits available to the dedicated yoga student.   When learning the asanas in a yoga class, you’re not simply learning how to arrange your body into a particular geometry, but rather how to simultaneously engage certain muscles and release others, while aligning the skeleton into a safely neutral position, breathing evenly... and doing all of this with awareness.  Attention on all of these subtle actions at the same time brings calm to the mind, while the actions taken bring vitality to the whole body.  

'Asana' is in fact just one of eight parts, though, of the whole path of yoga that originated in ancient India and is still practiced today.  (An Indian sage named Patanjali wrote down and described this entire eight-limbed path about 2,500 years ago --- it’s described in the second chapter of his ‘Yoga Sutras,’ or aphorisms.)   The first two limbs of the eight-limbed path of yoga are yama and niyama.  Within yama and niyama are ten moral and social precepts that guide the practitioner’s behavior:  'Be Truthful,' ‘Be Nonviolent,' 'Don’t have Greed,' etc.  Asana is the third limb of yoga, and these first three limbs together are considered the 'External Quest' of the eight-limbed yogic path.  The next five limbs of yoga are pranayama (directed control of the breath,) concentration, turning the senses inward, meditation, and finally the ultimate goal of Bliss, or Samadhi, or Union with God. These five limbs comprise an ‘Inner’ and then a ‘Spiritual’ Quest and take one on a more internal path if one wishes to consciously follow it.   

But what does expanding the chest in a back bend, or any other asana, really have to do with finding bliss?  Mr. B.K.S. Iyengar, the revered teacher of thousands of teachers and students around the world, explains that asana provides a venue in which to explore the other seven limbs of yoga.  Thus for example, while you are stretching your legs, arms and trunk in downward-facing dog pose, you might move the hands slightly outward (if necessary for your body) to help rotate the upper arms externally in order to prevent the shoulder’s bursal sac from being pinched, thus practicing nonviolence to yourself, one of the yamas.  In that same asana, for all students, having the head lowered brings quietness and invites an inward turning of the senses.  Also, attention to certain anatomical actions that make the pose vital (for example the drawing upward of the front thighs) promotes concentration, and if you are truly attuned simultaneously to several different actions at once (for example the grounding of the base knuckles of the index fingers and also the upward extension of the arms), you might approach a meditative state.  This pointed concentration and spreading of awareness is one of the things regularly pursued in Iyengar yoga classes.  Also, spending enough time in a given pose to learn the subtle actions so thoroughly such that struggle and tension are no longer part of it, even though the body is extended and full of action, brings the practitioner’s asana to a mature state of “effortless effort” which opens him or her to a state of being, rather than doing.  Mr. Iyengar, in his 70-plus years of practice and teaching, has learned on himself and wishes to teach that the eight-limbed path of yoga does lead to Bliss, as Patanjali wrote; and that such keen awareness of the body as learned in asana is a practical first step on a well mapped path toward coming face to face with one’s own true, eternal nature. 

You may or may not perceive this in your first, tenth or hundredth class, but you also may or may not be concerned, because you will in any case be basking in the benefits of flexibility, strength, a vital body, and a calmer mind.  

Further reading:
Iyengar, B.K.S.  Light on Yoga.  Shocken Books, 1979. 
Iyengar, B.K.S.  Light on the Yoga Sutras of Patanjali.  Thorsons, 2002. 
Iyengar, Geeta.  Yoga: A Gem for Women.  Timeless, 1990.