Determination is definitely one of the key aspects of the character of Santiago in this excellent novel, and can easily be demonstrated in terms of its meaning through his perseverance and unyielding attitude in catching the big fish that is his goal. A dictionary defines determination as "firmnness of purpose or resolve," and we can definitely see this in the patient yet determined way that Santiago fishes for his big catch--a fishing session that takes days and results in Santiago having to use every ounce of his energy, knowledge and perseverance to see it through to its conclusion. Note how, just before stabbing the fish with his harpoon, Santiago himself acknowledges exactly what his determination has cost him:
I am tireder than I have every been, he thought, and now the trade wind is rising.
Thus when we think of determination in the novel it is hard not to associate it with Santiago and the way that he carefully and painstakingly brings the fish in and manages to kill it.