The word has been given a variety of definitions over the years, everything from the pledging and hazing of college (and even high-school) students into fraternities and sororities to the admissions trials of secret societies, entry into occult and Masonic lodges and their grade or degrees, and to the more serious dramatic and transformative rituals of Wiccan and other esoteric groups. In some cases, the initiation rituals are truly effective in raising the consciousness of the candidate, whereas in other cases the initiation is more a certification of the levels of study and practice the student has mastered.
In the true Occult (and psychological) sense, Initiation is more an inner experience than an outer one, even though a dramatic ritual may induce an inner transformation and flowering of the psychic potentials and powers of the person. Despite the promises of various teachers, gurus, priests and adepts, it is less something done to the person and more something that happens "when the student is ready."
It has been called a "tearing away of the veil" so that the new initiate now sees with new eyes, and perceives a world of greater complexity, one of added dimensions, forces, and living beings. Progressive initiations mark further growth and development as the person becomes more of the Whole Person each of is intended to be. The potential is there from birth and before, and can be realized through knowledge, experience, and growth practices.
In the Theosophical concept, Initiation refers to a non-magical and more eastern process of expanding consciousness of which there are ten in number usually administered by an enlightened teacher. And maybe there are not enough of them to go around. Self-Initiation bypasses that shortage along with the high costs of travel and the possible dangers of international travel in troubled times. Even more are the dangers of attachment to a charismatic cult leader who provides an illusion of his own high adept status and an initiatory experience for his followers that must be constantly renewed.