Yoga is a Sanskrit word meaning "union of Atman (individual Self) with Brahman (Universal Self)." Atman and Brahman are both Hindu theological terms.
Interestingly, the Sanskrit root for "yoga" is "yuj;" i.e., "to yoke" [to the Spirit], and the Latin root for "religion" is "religio;" i.e., "to link-back" [to the Spirit]. Therefore it is a fallacy that "yoga" is not "religion" as the two words basically have the same meaning. With this basic understanding, it sounds almost as odd to say "I do yoga" as it does to say "I do religion." Fine—but which one?
Of course, it is in the Hindu religion that one finds all the many forms of Yoga. The Hindu religion (also known by the names Sanatan Dharma, "Vedic Dharma" and even "Yoga Dharma") is the spiritual foundation from which arose the Buddhist, Jain and Sikh Dharmas or religions.