The story and the telling of the story are two different things.
In other words, the narrator and the character in the story are not necessarily the same person. Oh, they have the same name and all that. But the narrator knows the story she is telling, while the character within the story does not. This provides opportunities that few writers explore.
I’ll use an old classic movie as an example of what I’m talking about.
By the way, moviegoers back then would know two things here: 1) the voice of the narrator is the star, William Holden; and 2) the man floating in the pool is William Holden. How is a dead man telling his own story?
These days, it seems the visible narrator—the one who almost seems to be there in the room with you, telling the story—rarely makes an appearance. But when done well, it can be so much fun! The best practitioners of first-person narration will use the telling of the story as a way to add to the tension rather than deflate it.
The easiest-to-find examples are in hardboiled detective fiction. One author who does it so subtly you don’t realize it is Raymond Chandler. Look inside: The Big Sleep. A completely different example is Charles Dickens’ Great Expectations Premium Edition (Unabridged, Illustrated, Table of Contents).
I’ll end with a made-up bad example to illustrate:
A man with a green hat pushed past me going into the grocery store.
The first time I saw the man with the green hat, he pushed past me going into the grocery store.
Two different ways to tell it. The first example stays strictly within the perspective of the character in the moment. The second, however, gives us some additional information that only the narrator could know—that this was the first time seeing this man, implying there were other times as well. It adds to the importance of the man in the story.
This approach opens other possibilities.
The first time I saw the man with the green hat, he pushed past me going into the grocery store. I didn’t notice the gun he wore on his hip.
And we’re off.
[Adapted from a Quora answer I posted the other day.]