Here are some definitions from source texts. Clearly these do not necessarily apply to the yoga we practice in yoga studios across the US. This applies to yoga as it originally came to be many years ago.

Via Christopher Wallis
Definitions of Yoga from the original Sanskrit sources

Pre-tantric definitions (8):

“Yoga is the [state in which] the fluctuations of the mind have become still.” Yoga-sūtra 1.2
“Yoga is the direct means to perceive Reality.” – anonymous ancient sūtra, cited in Brahma-sūtra-bhāṣya 2.1.3
“When the mind is dissolved into the Self, there is neither pleasure nor pain for the embodied one. This is yoga.” – Vaiśeṣika-sūtra 5.2.17
“Yoga is the liberation arising from the coming together of good knowledge, good doctrine, and good conduct.” – Yogaśataka 2 (Jain)
“Yoga is said to be equanimity.” / “Yoga is skill in action.” / “Yoga is severance of union with pain.” – three definitions from the Bhagavad-Gītā
“Yoga is the union of the self with God.” — Pañcārtha-bhāṣya

Tantric definitions (12):

“The word ‘yoga’ denotes nirvāṇa, the level of Śiva.” – Linga-purāṇa 1.8.5
“Yoga is said to be the oneness of one entity with another.” – Mālinīvijayottara-tantra 4.4
“Yoga is the attainment of identity with That.” – Svacchanda-tantra-uddyota 6.45
“To have self-mastery is to be a Yogi.” Mṛgendra-tantra YP 2a
“The term Yogi means ‘one who is necessarily conjoined with the manifestation of his [true] nature,’ in other words, the divine state….which is the invariable concomitant of self-mastery.” Mṛgendra-tantra-vṛtti YP 2a
“Yoga arises [spontaneously] from connection with Śakti.” – Parākhya-tantra 14.98
“Yoga arises from the attainment of samādhi.” – Parākhya-tantra 14.98
“Yoga is the immersion (samāveśa) into God arising from the contemplation of His nature.” – Parākhya-tantra 14.99
“Yoga is defined as the unification of the many pairs of opposites, [such as] the unification of in-breath and out-breath…the unification of the sun and the moon, of the individual self with the Supreme Self.” Gorakṣa-nātha’s Yoga-bīja 89-90
“A Yogi is one who has attained the mutual unification of the in-breath and out-breath.” Raviśrījñāna’s Guṇabharaṇī (Tantric Buddhist)
“Yoga is the realization of Śiva and the self as non-different.” – Śāradā-tilaka 25.2
“Yoga is the knowledge of the primordial Being.” – Śāradā-tilaka 25.3