c. 1600, "introduce to some practice or system," also "begin, set going," from Late Latin initiatus, past participle of initiare "to begin, originate," in classical Latin only in the sense "to instruct in mysteries or sacred knowledge." This is from initium "a beginning; an entrance," also in plural initia "constituent parts; sacred mysteries," a noun use of the neuter past participle of inire "to go into, enter upon, begin," from in- "into, in" (from PIE root *en "in") + ire "to go" (from PIE root *ei- "to go").
In some senses the English word is a back-formation from initiation. Related: Initiated; initiates; initiating; initiator.