Of all the character archetypes, I'd dare say this is the most common. This is a person who has entered a new situation, whether it is as a spouse, parent, employee, boss, discovering new powers, entering a new world, becoming of age to first experience something, etc.
This is often shown as the second phase in a character's journey. The first is innocence - they don't know what they don't know. But when a character becomes an initiate, they often believe their knowledge of reality is sufficient. Though an initiate will have had some kind of training, have some idea of expectation, they often are still quite innocent regarding the reality of what will happen. This can be seen in Jane Eyre, Luke Skywalker, Frodo, Jo March, Elizabeth Bennet, Harry Potter, Mulan, Belle, etc. Each of these characters had an idea of what they would expect and that is when the transition from an innocent to someone who is knowledgeable, wise even.
Some have said that the transition into becoming an initiate is brought on by one of three things: death, an awareness of evil or a sexual awakening. This seems strange, that it can be broken down to so few reasons, but if you look at the list of characters above, each of them experienced at least one of these. Just a quick rundown -
Death causes a character to be aware of mortality, the loss of someone close to them or a near experience of their own. This awareness cannot be undone and often launches a character into a plot to reconcile what the reality means with this understanding.
Awareness of Evil.
This may have been caused along with the awareness of death, or could be something else that bursts a characters bubble of innocence. It can be enhanced with an act of evil goes unpunished, making a character question what kind of a world could let such a thing happen.
Finally, sexual awakening.
Some people read this and think that it is alludes to sex in the most extreme circumstances. However, as soon as a character realizes they are feeling a level of attraction, as soon as that character starts behaving in a manner to capture the attention of whoever they are attracted to, they have become an initiate. This can be seen at the first attraction for younger age audiences to pursuing a boyfriend or girlfriend progressing all the way to the desire for a long term relationship.