What is "Hatha" Yoga? It is the practical Branch of Raja Yoga (the path to meditation) that includes the asanas and pranayama. It's practice is meant to bring the student to a place of stillness both within and without. The asanas are performed to prepare the body for sitting in meditation.
According to Alice A. Bailey in The Light of the Soul, Hatha Yoga has specifically to do with the physical body, it's conscious functioning and all the various practices with give man control over the different organs and the entire mechanical apparatus of the physical body. Ms Bailey continues that Raja Yoga synthesizes all the forces of the body in the head and from there distributes and controls them.
Yoga is the science of right living, and as such, is intended to be incorporated in daily life. It works on all aspects of the person: the physical, vital, mental, emotional, psychic and spiritual.
Asanas:
Certain specific body positions that are related to yogic practices. It is thought that they open the energy channels and psychic centers of the body. Asanas release mental tensions by dealing with them on a physical level. The result is that the body becomes full of vitality and strength, the mind becomes light, creative, joyful, and balanced.
Pranayama:
Generally defined as breath control. The word pranayama is comprised of two roots: prana plus ayama. Prana means life energy or life force. Yama means control however, Ayama is defined as extension or expansion. Pranayama means extension of of the dimension of Prana.