What is the meaning of yoga?
Commonly translated, yoga is a union of the body, mind and spirit. It is the union of prana with apana; the union of the sun with the moon, or light with darkness. It is a union of masculine and feminine, inhalation and exhalation, the union of the thoughts of all people. In using the word union, what is truly meant is unification of dueling energies or opposites, creating balance. Ultimately what we are striving to learn is that it is not possible to have no thoughts and so we seek to still the mind down to simply one thought. "yoga citta vritti nirodha" translates as "yoga is the control of thought waves in the mind".

What is Ashtanga?
According to Patanjali (the 1st ancient sage to document this tradition), ashtanga refers to the 8 limbs of yoga. These limbs evolve from the physical and mental to elevated states of meditation. The limbs are complete upon reaching "samadhi", union or enlightenment. The limbs are listed in Patangali's text known as the Yoga Sutras. II:29
Yama (restraint)
Niyama (observances)
Asana (steady posture, or posture easily held)
Pranayama (science of breath)
Pratyahara (withdrawal from the senses)