This is the idea that many forms of knowledge cannot be acquired without experience. There are places where words, descriptions, actions fail to capture the entirety of experience - where the mind cannot go without having first been there in the flesh.
Imagine taking a primitive tribe member, or somebody from the middle ages to Tokyo and you have the idea, his or her language won't contain the words or the ideas necessary to describe their experience.
The most well known example of initiation that I can think of is the Garden of Good and Evil, where Eve begs Adam to taste of the fruit of the knowledge of good and evil. This is initiation in the purest form - once tasted there can be no going back, and one has entered into a whole new world of opportunity and experience.
Initiation, here it should be noted, is often - almost always - described symbolically or metaphorically. Remember we are here discussing experiential knowledge that cannot be acquired through reading or other means.
Now - Initiations fall into a broad range of categories, which I will summarize here - most of them merely ape other, greater initiations or indoctrinations, or are done more for the sake of the audience than they are for the participant.
- In this class we have the Seven Sacraments of the Catholic Church - Baptism, Confirmation, Eucharist, Confession, Anointing of the Sick, Holy Matrimony and Holy Orders. These - for the most part, are done for the social benefit, the Church has too long obscured the real meanings behind the Sacraments and so they remain veiled even for the recipient.
- We also have the Initiations into public office, the Keys to the City, the Swearing in of the President, Pageantry and seals of office, other processes of officialdom. It is possible, although unlikely, that with these initiations there comes a deeper knowledge or understanding of the privileges and responsibilities of office, but it would appear from the general behaviors of the initiated that - No, this is purely formality and ceremony.
- And then there is the initiations into sports teams and sophomore fraternities, where the initiation creates generally through the shared bonds of shame acceptance into the group.
The above forms of initiation cannot be considered, in any real or meaningful way, initiations. They have fallen into the pattern of tropes or convention, there is no wider awakening into a greater world.
Consider, however, tribal initiations - coming of age ceremonies, where a member will be sent into the wilderness to fast and discover ones identity and purpose. This is closer to what we mean. I remember reading of one tribe where the children, upon becoming men, were taken by the elder men of the tribe into the forest to have their asses sewn up so they could no longer fart, the initiation, presumably, was one into the world of adult hypocrisy, and an eye-opener it must have been.
In pop culture there are countless references to initiation - Neo, in the Matrix, "Red Pill or Blue Pill", Luke Skywalker meeting Obi Wan Kenobi, Tom Cruise in "Eyes Wide Shut" - who, while initiated is rejected from the group - and rejects the group as well, preferring to return blindly to the world he left.
Expressed in art we have things like the Chinese nesting Ivory Balls, or the Medieval view of the Universe, stars and planets hung upon a concentric rings of crystal spheres, the hinting of hierarchical layers of consciousness, while the Medieval view frequently portrays the man looking out upon the spheres from earth, the Chinese nesting balls allows one to handle the universe and look in upon man.
Consider, too, mathematics - which allows for the expression of ideas which language can only circumvent, while we learn numbers and maths in such a way that is gradual - there is no initiation, or larger "ah-ha" moment, there are opportunities to imagine it. "Flatland", by Edwin Abbott, attempts to explain the mystery of the Church through Mathematics, the comprehending of extra dimensions from a two dimensional (or three dimensional) perspective, mathematics can describe this easily, on a simple spreadsheet we can map out countless dimensions, but the real understanding eludes us, there exists no corollary in our experience that can make us really understand.
Drugs offer, to those inclined, an invitation to an initiation of sorts - consider an impressive LSD, DMT or other Psychedelic experience - explaining this to someone who has never had it will fall on flat ears, they can't really understand. And people who have that experience will - oddly enough, because of their shift of perceptual standards, will understand. Initiations of this sort are commonly described - and warned against - in folk-tales and literature, consider that if, while reveling with fairies, you should partake of their food or drink you will be forever bound to their kingdom and unable to return. Or Rossetti makes the same argument - metaphorically - to sexual initiation in "Goblin Market", in which once you've tasted of the pleasures you will be unable to return to ordinary life.
There are, of course, countless references to spiritual epiphanies which require no elaboration, these epiphanies are of course initiations as well, but their being sanctioned by the Church creates a validity denied other awakenings.
And there are the inadvertent, unsolicited epiphanies which occur without solicitation, they are more seen as "invitations" available only to a select and limited few - the sighting of a Bigfoot, UFO, Ghost or other such bogie to an otherwise rational person would be an initiation of sorts, depending on how they choose to interpret the event. And note that a great many people go out - on ghost hunting tours, bigfoot hunting tours, spotting for flying saucers, yet are denied the initiation - which is a curious thing...