Hemingway explained his own style only a handful of times in print, and the clearest explanation he ever gave used an iceberg.

The Direct Answer
It's Hemingway's idea that a writer can leave out most of what he knows about a story and the reader will still feel it, as long as the writer understood it well enough to cut it on purpose.
He laid it out in Death in the Afternoon in 1932, comparing the visible part of a story to the one-eighth of an iceberg that sits above water.

The Original Statement, in His Own Words

The theory doesn't come from a letter or a late-life interview looking back. It's in Death in the Afternoon, his 1932 nonfiction book about bullfighting, tucked into a passage that's ostensibly about something else altogether. Hemingway used the bullring to make a point about writing, and the point has outlived the book it appeared in by a wide margin.

If a writer of prose knows enough about what he is writing about he may omit things that he knows and the reader, if the writer is writing truly enough, will have a feeling of those things as strongly as though the writer had stated them. The dignity of movement of an ice-berg is due to only one-eighth of it being above water.

Ernest Hemingway, Death in the Afternoon, 1932

Notice the condition buried in that sentence. Omission only works if the writer knows the thing being left out. Cutting material you never understood in the first place just produces a hole where the depth should be. The theory isn't a license for vagueness: know more than you're going to say, then say less than you know.

What It Looks Like on the Page

You can see the theory working in Hemingway's short stories more clearly than in the novels, because the compression is more extreme. Hills Like White Elephants never states what the couple is arguing about. A reader who's paying attention understands anyway, because the dialogue is built by someone who knew exactly what was underneath it and chose which eighth to show. Strip out the unstated subject and the story would collapse into a description of two people arguing about nothing in particular.

The technique is why Hemingway's prose reads as spare without reading as thin. Plenty of minimalist writing feels empty because there's nothing under the surface to imply. Hemingway's omissions work because the seven-eighths he's not showing you are fully worked out in his own understanding of the scene, even if not one word of it makes it to the page. The gap between what's said and what's known is where the story's weight sits.

For the desk, the pencils, and the rest of how a day's writing actually happened, see the full Ernest Hemingway writing routine.

What You Can Steal