The word Yoga has such a vast meaning and there are numerous interpretations that can be found. I'll attempt to give my students a meaningful, comprehensive definition. Yoga is both a practice and a state of being. It is the systematic, defined practice of achieving the state of yoga, which is perfect balance and harmony, so that the individual soul (atman) can merge with the supreme soul (paramatma), and ultimately attain Moksha (liberation). We practice yoga to achieve yoga.
As there are numerous interpretations of the word Yoga, there are equally as many paths of yoga practice, the most common being the system defined by the well-known "Father of Yoga", Patanjali. Patanjali founded Ashtanga Yoga, or the Eight-Fold Path, defining Yoga as a practice to develop the body, mind, and intellect, in order to go beyond them and find the immortal soul - or satchitananada - truth, knowledge, bliss, which is our true nature and the ultimate goal of life per hindu scriptures.
To be on the yogic path, one must develop the following:
-- A perfectly healthy body with all internal organs and systems functioning optimally
-- A clear and pure mind, where the individual is in control of his thoughts, and not enslaved by the seemingly uncontrollable and never-ending thought process
--A strong and brilliant intellect with the skilled power of discrimination
Patanjali's Yoga Sutras clearly state how to achieve the above through practice of yamas, niyamas, asana, pranayama, dharana, and dhyana which lead us to samadhi / moksha.
Simply performing asana is not yoga in the true sense. Yoga as a fitness regimen is different from the Yoga as a practice to attain spiritual upliftment and freedom from the material world, including our senses. Yoga in its true meaning is union with God, or the path to get there. However, asana does have a significant role in Yoga sadhana. We must have a healthy body, clear of any pranic blockages, free of pain and disease, so that we can clear our mind. It is almost impossible to meditate with a clear mind if one is experiencing pain or discomfort. But asana must be accompanied with pranayama and also proper yogic diet to keep the body in perfect health. In 2nd century BC, when Patanjali was predicted to live, diets were pure and natural and according to season, in line with ancient herbal practices. It was perhaps not necessary to outline what a proper diet was, since people ate to live, and not lived to eat. Today it's of the utmost importance.
While asana is not yoga, and yoga is not asana alone, asana is part and parcel of a yogic practice. Practice yoga, the eight-fold path, as much as possible and start to see the true benefits of hatha yoga, such as peace of mind and a feeling of satisfaction, fulfillment and bliss.