This memory of Santiago when he arm wrestled the famous negro from Cienfuegos is actually a very moving part of the book, as it shows Santiago in his younger, stronger days. What is so moving about it is that the text deliberately suggests Santiago summons this memory in order to strengthen his resolve and courage in the current struggle that he faces. Note what the text says:

As the sun set he remembered, to give himself more confidence, the time in the tavern at Casablanca when he had played the hand game with the great negro from Cienfuegos who was the strongest man on the docks. They had gone one day and one night with their elbows on a chalk line on the table and their forearms straight up and their hands gripped tight.

The phrase "to give himself more confidence," draws a parallel between the struggle in the past he faced and the struggle in the present that he faces now. Just as Santiago had his arm locked with the negro's arm in the past struggle, so now his arms are locked as he faces his present struggle with the fish that he is trying to bring in and kill. The overall impression we receive of Santiago is an incredibly determined and resolute man who is not used to giving up, and who has immense patience and fortitude. This impresses the reader immensely, and the text presents Santiago in a way that the reader can only admire and be in awe at.