The simile is trying to get us to visualize Santiago's wizened old hands and what they represent. He's an old man, a fisherman who's been out to sea goodness knows how many times over the course of his life. Inevitably, after all that time and all that fishing, his hands will be covered in scars. But not just any old scars. As Hemingway points out, they are

[D]eep-creased scars from handling heavy fish on the cords. But none of these scars were fresh. They were as old as erosions in a fishless desert.

Note the key words here. "Old" emphasizes not just Santiago's age, but how long he's been a fisherman. It also refers to the fact that it's been such a long time since the old man landed a really big fish. And this means that, for Santiago, the sea is now virtually a "fishless desert." Just as the sea has dried up, no longer yielding up its riches, so too has the old man's life. The scars on his hands aren't fresh, because he's no longer fresh; he's not a young man anymore. Santiago's old, gnarled, scar-riddled hands symbolize what he's now become.

This line ends the second paragraph, describing Santiago's physical appearance. It and the other descriptors serve to show Santiago's age and the way his experiences have shaped his personality and his face:

The old man was thin and gaunt with deep wrinkles in the back of his neck... The blotches ran well down the sides of his face and his hands had the deep-creased scars from handling heavy fish on the cords. But none of these scars were fresh. They were as old as erosions in a fishless desert.
(Hemingway, The Old Man and the Sea, Google Books)

The reference to "erosion in a fishless desert" is a metaphor that capitalizes on both Santiago's age and his profession. Santiago is old, and the scars and wrinkles in his face and hands are the result of a long association with the sea. Erosion is usually a result of water; while desert sands can erode from wind, this more likely refers to the old oceans that used to cover many deserts, and the eroded bedrock underneath the sands. Those erosions have been there since there were fish in the desert: a very long time ago. Similarly, Santiago's "erosions" started when he was young, and are now as old as the life he has spent on the water.