The Iyengar method of Yoga is initially learnt through the in-depth study of asanas (posture) and pranayama (breath control).
Mr Iyengar has systematised over 200 classical yoga Asanas and 14 different types of Pranayamas (with variations of many of them) from the simple to the incredibly difficult. These have been structured and categorised so as to allow a beginner to progress surely and safely from basic postures to the most advanced as they gain flexibility, strength and sensitivity in mind, body and spirit.
In summary, the Iyengar method of Yoga may be said to define itself as different from other styles of Yoga by 3 key elements, namely technique, sequence and timing:
Technique means that in practice one learns ever finer adjustments in the alignment of how one performs one's asana and pranayama. Sequence refers to the sequences in which asana and pranayama are practiced. For example, by varying which postures are practiced after which, the mental and emotional effects of the practice can be intensified in a manner not otherwise possible in order to bring about changes to the whole being including ones spiritual evolution. Timing refers to the length of time spent in postures or pranayama. Postures cannot be done swiftly or without awareness. It takes time to move into a posture and become stable. When this has been achieved then one remains stably for some time to intensify the depth of the posture and so extract its benefit. Otherwise the potential effects and benefits remain small compared to what is possible.
So one can begin to see how Iyengar yoga cultivates all 8 disciplines of yoga and is far from merely "gymnastics and deep breathing." With practice and understanding, one realises that Asana (posture) is as different from stretching or gymnastics just as Pranayama (Breath control) is different from merely deep breathing and meditation is different from self-induced trance.
The prolonged practice of asana and pranayama affects the individual on an organic (physiological), mental and spiritually level as well as just physically.