The author uses third-person omniscient narration, which means the narrator hovers "godlike" over the story, knowing all that is going on. He is able to give us background information and can flit in and out of different people's heads. We see this in action in the opening of the novel:
He was an old man who fished alone in a skiff in the Gulf Stream and he had gone eighty-four days now without taking a fish. In the first forty days a boy had been with him. But after forty days without a fish the boy’s parents had told him that the old man was now definitely and finally salao, which is the worst form of unlucky, and the boy had gone at their orders in another boat which caught three good fish the first week. It made the boy sad to see the old man come in each day with his skiff empty . . . .
As we understand, the narrator gives us background: we learn directly and simply that the old man has not caught a fish in 84 days. Hemingway doesn't have to contrive dialogue, for example, to communicate this to us. We also move quickly to what the boy's parents have to say, and then into the emotions of the boy (sad).
The great advantage of third-person, omniscient narration is flexibility. There are no limits on what the reader can be told, because the narrator has no limits on his ability to know what is going on. Hemingway, nevertheless, tells most of the story from the old man, Santiago's, point of view, describing what is happening to him as he perceives it and letting us know his thoughts.
Hemingway uses a very spare, simple style of narration. This makes the story easy to follow and conveys a sense of Santiago's Christlike purity of heart. The simple narration supports a simple, straightforward story: Hemingway doesn't have to tie himself in knots to communicate information: he can simply directly tell us what he wants us to know.
A disadvantage to third-person narration is the distance it can put between the reader and the action. If we think of different types of narration as different ways of filming a scene, first person means the camera is always on the narrator's shoulder, so we always see everything up close and personal. In third person, the camera is everywhere: we can get long shots and panoramic vistas, which can be nice, but such shots also lack immediacy.
Primarily, Hemingway's narration in this novel works very much to his advantage. It's a case of form fitting function.