The warbler story is about how age and experience affect personality and ability. While Santiago fights the strong fish, a young warbler comes to sit on his line. It seems exhausted, and Santiago wonders if it is the bird's first trip across the bay; on a calm day, with no strong winds, the bird shouldn't be so tired. He wonders if the bird knows yet about the hawks that ride the high thermals, waiting for smaller birds to catch.

"Take a good rest, small bird," he said. "Then go in and take your chance like any man or bird or fish."
[...]
You did not stay long, the man thought. But it is rougher where you are going until you make the shore. How did I let the fish cut me with that one quick pull he made? I must be getting very stupid.
(Hemingway, The Old Man and the Sea, Google Books)

Any activity, whether traveling across the bay or catching a large fish, is filled with risk. The bird's first trip across the bay might end in disaster, or he might make it safely, or he might barely escape a dropping hawk. If he sees the hawks, he will be better prepared for the next trip. As a person ages, the mind and body slow down, becoming less suited for hard mental or physical work. Santiago, realizing that he let his mind slip and was injured as a result, knows that even in old age he must resolve to be strong of mind and not release the line; all he can do, Santiago realizes, is take the chance, just like the bird. If not, he has lost his entire life to old age, and all his experience counts for nothing.