Using Satyananda's Yoga Magazine as a resource, here is their definition of hatha yoga:
"The term Hatha Yoga has been commonly used to describe the practice of asana (postures). The syllable ha denotes the pranic (vital) force governing the physical body and tha denotes the chitta (mental) force thus making Hatha Yoga a catalyst to an awakening of the two energies that govern our lives. More correctly the techniques described in Hatha Yoga harmonise and purify the body systems and focus the mind in preparation for more advanced chakra and kundalini practices.The Hatha Yoga system includes asana along with the six shatkarmas (physical and mental detox techniques), mudras and bandhas (psycho-physiological energy release techniques) and pranic awakening practices. Fine tuning of the human personality at increasingly subtle levels leads to higher states of awareness and meditation. Hatha Yoga has been described in several classic texts, notably Hatha Yoga Pradipika and Gherand Samhita."
In order to benefit from the great science of hatha yoga, I believe it helps to understand that it is a way to prepare ourselves for spiritual awakening AND it is also a science of health.
When Richard Rosen visited Richmond, he gave an excellent talk entitled "Introduction to the History of Hatha Yoga" which I encourage you to listen to here. If you have ever spent time with Richard, you know that his knowledge of yoga is extensive.
There is so much to understand that I'm going to stop writing and leave you to your reading and listening and encourage you to follow your own path. Find a teacher, practice, read, love yourself, practice some more, and watch what happens.