Narrative Distance: the distance between a reader and a narrator in a story.
In most high school classrooms and literary analysis, most emphasis is placed on narrative point of view. What isn't mentioned very often until/unless you are in a writing program is a concept called "narrative distance," and it might actually be a more important idea to understand for a writer.
Conventional writing wisdom suggests that if you want to be "closer" to the narrator, you pick first person and if you want to be "further" from the narrator, you use third person omniscient. This is overly simplistic and borders on simply untrue.
While the narrative point of view can influence distance, it in no way determines it. Yes, first person narration is generally closer but it doesn't have to be if the narrator is keeping emotional distance. Distance is best thought of as a completely different axis of narration that refers to the space between the reader and the narrator of a story.
Because narrative distance can be close or far regardless of point of view.
Consider a book like Ishiguro's Never Let Me Go: though it is in first person, the narrator is looking back many years from the time of narration to the time where the events of the book take place. She regularly admits not being able to remember things, and drizzles in some perspectives that have come from years of reflecting on these events and weren't in her head as she's narrating. She sometimes even hints at what is going to happen next because it's been years since these events and she KNOWS what happens next.
On the other hand, the narrative distance in G.R.R. Martin's Song of Ice and Fire books, despite being in third person, is deep within one particular character's head for each chapter––even influencing whether they notice esoteric details or food or clothing or apparent fighting prowess more than other things. Their thought processes are written out.
First person close: I opened the door. My heart stopped and the world swam before my eyes. It was my brother. And he was clearly dead.
First person distant: Opening the door turned out to be the worst decision I made for many years to come. I found my brother's corpse on the couch.
First person (very) distant: I opened the door to my apartment like it was any other Saturday morning. My brother's corpse was splayed on the couch. I staggered for a moment before starting forward.
First person (very) close: I threw open the door. My brother. Vision swimming. Balance twisting. Heart frozen in mid squeeze. My brother....dead.
Third person (very) close: James opened the door. What was that on the couch? Was it a person? Oh god, it wasn't just any person, it was his brother. And very clearly dead. James's heart clenched closed for a suspended moment. His vision leapt left and right, up and down.
Third person distant: What James would find on the other side of the door that Saturday would rattle him to his very core. His brother's body, clearly dead, sprawled across the couch.
Third person (very) distant: When he was twenty-one James walked into his apartment one Saturday in May to discover his brother's body in an advanced state of decay. It would take years after that for James to not take a girding breath before opening a door.
Notice how the language changes. Notice how the immediate thoughts and physiological reactions are focused on in the closer readings and left out of the more distant ones. Notice how you get more detail on the distant but less emotional resonance. Notice how we're right in James's head for some third person readings, but we can focus strictly on actions even in a first person narration.
Now let's look at John Garner's five levels of examples of this in The Art of Fiction (although he calls it "psychic distance):
1 It was winter of the year 1853. A large man stepped out of a doorway.
2 Henry J. Warburton had never much cared for snowstorms.
3 Henry hated snowstorms.
4 God, how he hated these damn snowstorms.
5 Snow. Under your collar, down inside your shoes, freezing your miserable soul.
While the fifth level obviously takes some second person liberties, all of these are in third person and yet get closer and closer.
Many stories "pan" in and out between close and distant narrative distance. Often moving closer for emotional moments and further away to cover more ground quickly. But very often the narrative distance is an important choice in how the story unfolds.
Imagine telling a story from your point of view an hour after it happened when you were mad at someone. Now imagine telling it (still from your point of view) a year after it happened and you realized that you were actually the one being the jerk. How about 20 years? Can you rightly say you were even the same person twenty years ago that you are today? Very different stories and something an author has to consider depending on how they choose to craft their narrative.
Similarly a third person narration may focus on the action of a character and the physical description, or it may go deep into their head, even bringing the reader along in the actual thought process. This could be the difference between the main character being a monster telling the story from its own point of view, or having the fact that the character was the monster all along be the "twist" ending. Two VERY different stories (even if every plot point is identical).
And of course, one of the sly tricks writers pull is to add just the tiniest hint of authorial judgement to a third person close narration.
Internal Monologue- Most internal monologue is not the shift-to-italics-and-quote-the-exact-thoughts variety. You don't see that much, and even less in modern writing. Usually it's more subtle. (James walked around the building looking for a way in. The Pendercots were exactly the kind of meticulous people to keep a Hide-a-key. All he had to do was find a rock that didn't look like any of the others...) See how that is right in James's thoughts but without being like: (Come on, James. I thought. The Pendercots are anal about everything. They have to have a hide a key. Find a rock that looks different than all the others.) The irony here is that the latter is generally GREATER narrative distance. By separating the reader and the thoughts like that, you are not inviting the reader to come in to the head space, but only giving them glimpses.
Consider logistical details- Notice in the above examples that the logistical details increase with the narrative distance. Some of them are so close they don't even mention the couch. If we're in someone's head during an emotional event, it is less normal to think of those kinds of details. Consider going to your local grocery store. You just GO, right? You don't think about how you get there or what street it's on. So the addition or subtraction of these details can help you establish your narrative distance.
Consider your vocabulary- If you are doing distant first, is your character describing an event from before they had went through puberty but describing it AFTER they were an old man? A PhD describing a childhood memory will be very different than a ten year old describing what happened five minutes ago. If you are in your character's head, it's going to sound like your character's thoughts. Do they have your vocabulary? What would they use to describe things? If you use florid language in your descriptions and your character is a much simpler person, you are creating narrative distance with your reader you might not intend.
Consider "Show, Don't Tell"- One of the reasons this advice is great for starting writers and increasingly problematic for more experienced ones is because it presumes a close narrative distance. At a close distance, you will want to show more details because you want the reader to experience what the character is, but you can "tell" a LOT at a great narrative distance.
Consider what your character would care about- This is going to dovetail with the concept of significant detail, and the closer your narrative distance, the more this significant detail is crucial in helping to characterize your focalizer character. If your character is a germaphobe, they should notice dirt and grime and people leaving the bathroom without washing their hands. A distant narration might be less interested in these details or only mention the character's discomfort at them. A distant first person narration may have new priorities and be remembering events through a different lens of priorities. In "Penumbra," my character narrates post epiphany, and often questions some of his own earlier thoughts.
Consider filters- Filtering words like "noticed," "saw," "observed," "remembered," "recalled," "thought" (and many many more) increase the narrative distance.
Why does narrative distance matter? The short answer is sympathy. The closer you go, the more sympathy you are asking for from your reader for your character. While that's usually good if you want it (and want it THEN), it's not always the right choice. Many great stories can be told through the filter of time or the filter of redemption or with a distance that allows a less sympathetic character to still be compelling in less interesting ways. "I was once an asshole," is an important trope in fiction. However, the closer you are to a character, the more you are making a deal with your reader that they will BE that character for a while, and sometimes that's not what you want. And sometimes that's exactly what you want.