Atha – now….we begin, here it is or auspicious blessing
Yoga – harmony, balance, clarity, union, gathering, ability, altitude, joining, combination, application, deep meditation
Ānuśānam – instruction that has authority, instruction from experience, prescription, teaching transmitted from master to disciple through generations
Here it begins the authorative instruction of yoga
With prayers for Devine blessings, now begins an exposition of the sacred art of yoga
This is where we begin the journey along the path of yoga that has been laid out by many before us
Patañjali introduces yoga in his first Sutra, by using the word atha he is bringing it to the present but also giving it a meaning that's deeper than the surface level by making it a blessing.
Anuśānam gives the sutras depth, it states that Patañjali did not make these up, or design yoga. He is mearly passing on the practice he has experienced within his lifetime and has been handed down through the ages by his teachers and the teachers that came before them.