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.