Webster's Dictionary 
(1): ( n.) The act of initiating, or the process of being initiated or introduced; as, initiation into a society, into business, literature, etc.
(2): ( n.) The form or ceremony by which a person is introduced into any society; mode of entrance into an organized body; especially, the rite of admission into a secret society or order.
Cyclopedia of Biblical, Theological and Ecclesiastical Literature 
a common term in the early Church for baptism, having reference to the full instruction in the mysteries of Christianity which was given to the baptized, but withheld from the unbaptized. The baptized were thus called initiati, Οἱ Μεμυημένοι , Μυσται , or Μυσταγώγητοι ; and it is very common to find the fathers using the expression "the initiated will understand" in their preaching to mixed congregations, especially when they were speaking of anything which belonged to the doctrine of the holy Eucharist. This expression is said by Casaubon to occur fifty times in the sermons of St. Chrysostom alone. — Blunt, Theolog. Dict. 1, 348. Several other names were given to these persons, such as Πιστοί , fideles, Φωτιζόμενοι , etc. The word has sometimes been employed with reference to the supposed duty of Reserve in communicating divine knowledge, as though the holy Scriptures justified the withholding instruction in Christianity from persons in an early stage of their Christian course. — Bingham, Orig. Eccles. bk. 1, ch. 4: § 2. (See Disciplina Arcani).