Santiago has spent two days holding the line while the marlin swims in a straight line, tiring itself out. The marlin is so big that Santiago must be pulled behind it, and cannot pull it in until it is dead. On the third day, the marlin begins to circle, showing that it can't keep swimming against the current:
He could not see by the slant of the line that the fish was circling. It was too early for that. He just felt a faint slackening of the pressure of the line and he commenced to pull on it gently with his right hand.
(Hemingway, The Old Man and the Sea, Google Books)
This behavior proves to Santiago that the marlin is on its last reserves of strength, and that it will soon come to the surface where he can harpoon it. The marlin is strong enough to pull the boat, but it can't pull forever without resting; the circling behavior shows that it is losing strength because Santiago never lets the tension of the line go.