The words adi vani are Sanskrit. According to the Monier-Williams Sanskrit Dictionary, adi means “beginning” or “first,” and vani means “sound,” “voice,” “words,” “literary composition,” and so on.
So adi vani can be taken to mean “original words.”
Sometime around 2003, a group of “Hare Krishna” people began using the term to promote their editorial views about the books of His Divine Grace A.C. Bhaktivedanta Swami Prabhupāda, Founder-Acharya of the International Society for Krishna Consciousness.
The term never appears in Śrīla Prabhupāda’s books, and we have no evidence he ever used it.