Yoga literally translates as yoking, meaning union or connection. This connection is meant to be with the higher self or spirit and with God. I also believe it means a connection and respect for all life.
More than that yoga is freedom and liberation.
In the words of Patanjali (yogic philosopher credited with writing the first yogic text), yoga is the stilling of the restlessness of the mind.
Yoga is peace, kindness, joy and gratitude.
Yoga is breath and movement.
Yoga is balance.
Yoga can be anything you want and need it to be, from the simple breath and doing nothing (but paying attention) to self study to meditation in motion to exercise and much, much more.
Yoga is everything and nothing.