One thing that fiction makes possible, and that makes fiction interesting, is the way it can show how what feels, in real life, like a simple and unified interaction with others occurs on several channels at once. Fiction mutes some of those channels, and therefore focuses our emotional attention, our attentive emotion, on those that remain. And it focuses the theorist's attention (as here) on the differences between those channels that remain open and those that are muted.
For example: in a play we and several hundred other people in an audience can be in the presence of a character who is entirely alone. The channel of their presence to us is open; the channel of our presence to them is muted (although not entirely). At a movie we can hear everything that one lover whispers to another in the absolute privacy of some erotic sanctum. (Our presence to the characters is completely muted, though our presence to the actors only partly so.) The way these figures are present to us when we are not present to them is what I mean by the separation of one channel from another. Usually, in the real world, presence is a commutative relation. If I am present to you, you're present to me. (Even sleeping isn't a counterexample: If I'm asleep and you're awake, neither is present to the other.) But in fiction this apparently axiomatic double relation is no longer one (that is what makes it fiction).
This general idea allows us to see that first person narrative, at least since the nineteenth century, will frequently involve a narrator presenting herself to us in written words that she has never been supposed to have written. The written words are the way she's present to us; her never having written them is the way we're not present to her, since she never addresses us in her world. The channel in which her words exist is the channel we receive on, not the channel she receives on, even if she's writing.
It might be useful to establish a couple of preliminary distinctions in our vocabulary to help keep us clear on this issue. First, distinguish between a true first person narrator and a false one. What I am calling a false first person narrator is really just another character (focalized as much as you like) whose utterance a third person or omniscient narrator reports. Clarissa reports the letters that it collects, and all the first person narrative in those letters may be thought of as quoted discourse. (The true first person narrator of Clarissa, the narrator who addresses us or such as us, is the putative editor of this correspondence.) Poe quotes the full MS that Arthur Gordon Pym has written. But Ishmael addresses us directly in Moby Dick. We can then establish a pretty strong boundary (it's not absolute, but its breach, as in Proust, is always interesting) between what it may be useful to call true narrators and reported narrators.
Let's also distinguish between a character (in the sense of personality) and an agent. Usually this distinction will count most when applied to a true narrator. The narrator will do things in the work she narrates, will be an agent in that narrative (interacting with other agents, as, for example, when Nick brings Daisy and Gatsby together). Insofar as she does that, she's an agent as well as a character or personality.
All agents are characters but the two terms are not synonymous. We can separate off the idea of character by noting that part of out sense of her as a character (part of the fiction's presentation of her as a personality) is established or nuanced or complicated by what she says to us, even though she does not say these things in the world she lives in, wholly lives in, as an agent. The shocking moment that Nick talks of Gatsby's "appalling sentimentality" tells us much about Nick, but doesn't affect the plot of the book.
So a narrator's tone, judgment, voice, expectations, and so on, all affect our sense of the narrator as a character and so also affect our sense of the narrator as agent, even though these things do not belong to her as an agent within the fiction.
This leads to interesting and I believe somewhat unexpected insights. I've noted elsewhere how interesting it is that despite the fact that we can make the distinction between narrator and agent it's not quite absolute. It almost always seems to violate fair play to have a true narrator die (as in Susannah Moore's Whiteness of Bones [highlight if you don't mind the spoiler: not a great book, but still]). Ishmael must escape to tell us, even if he doesn't tell us as an agent. How else could be be narrating? It doesn't matter that we don't expect the narrator to have ever written the words we read, perhaps none of them. We still require that the voice which addresses us belongs to a character (NB: not to an agent) who is still alive, still exists, still can speak. Usually, in a written text, we require that it belong to a literate character, one who could write what we're reading. (Norman Rush's dialect works may provide a counterexample, but it's also possible that we process works narrated in a dialect we know not to be the author's as narrated by what I called a false first person narrator.) The Murder of Roger Ackroyd offers more to think about: the narrator just sounds too different from the agent designated by the same first-person pronouns for everyone to feel comfortable with the trick Christie plays. True first person narration occurs in some modal, subjunctive world.
Not, though, a possible world: the point is in no world does the frue first-person narrator actually write the narrative. We see no contradiction in such last sentences as: "She asked me to promise I would never tell anyone any of this [what we've just read], and that's a promise I'll always keep." But in no possible world could that sentence seem innocuous. It always and knowingly bridges two worlds (as Lewis says we mustn't).
Borges's "Secret Miracle" is relevant here, at least as an emblem of what I mean, or perhaps its reciprocal converse. The miracle is the work; the secret is its non-existence in the world in which it's written.
I'll note one minor but interesting effect of this muting of full commutative communication between fictional addressor and us real addressees: It makes a certain kind of boasting possible. Richard III and Iago, in their various soliloquies, rejoice in being able to act like the "formal vice, Iniquity," rejoice in their own cleverness, in being tricksters. Had they boasted as agents, in the worlds they inhabit, they would, by the laws of narrative (in our culture anyhow), inevitably fail. Boasters get shown up. Soft-spoken understaters surprise.
But the boasting they do is not boasting in their world. They boast to us, not to their compeers. And so they are setting forth the parameters of the challenges they will meet, doing it for us. The magician's relish they take in difficulty is something we need to know. It wouldn't work in their world, but it does in ours. The difficulty and boasting are present to us, but not a presence in the world they inhabit.
Since I think this situation, this non-commutative presence, is the key issue here, we can say that all these moments: narration, boasting, the privacy and unawareness of figures in fiction, are paradoxically enough, versions of the same thing. Richard's boasting and Isabel Archer's silent thinking are really different manifestations of one relation to us.
It's no wonder if this seems like our beliefs about our parents' attitude towards us. For in real life, that non-commutative relation to others is what the child believes about its parents. I am not fully present to them. They transcend me. Yes, they sometimes ignore more and sometimes boast to me and sometimes rebuke me and sometimes tell me about themselves. But in none of those cases am I interacting with them in the world they truly live in, as agents. All the evidence that they give me of being focused on me is worth as much or as little as the evidence that fictional agents give of being aware of me. Fiction is possible, in part, because it repeats a relation we have to those greatest of fantasy figures, the actors in the family romance of which we are in the end spectators (so we think). And fiction shows how the family romance can work, through the separation of those things that serious adults, living real lives among real people, forget don't always come together, not, anyhow, in the awe-struck, humble eyes of the child, all absorbed in the fantastic world it is not and cannot be part of.