The lions symbolize youth, strength, happiness, and hope for the old man.
Santiago's dream about the lions is first described in the opening fifteen pages of the book. He used to see the lions playing on the beaches of Africa, where he grew up, and he remembers that "they played like young cats in the dusk and he loved them". In the midst of his epic battle with the big fish, Santiago again dreams about the lions, and "he (is) happy".
The significance of the book ending with a final reference to the dream of lions is that it shows that the old man, although battered and beaten possibly to the point of death by his encounter on the sea, still retains the ability to hope and dream - of returning to the challenges of life, of celebrating once again the vigor of his youth, of living like the "young cats" frolicking on the sand. The story ends on a positive note, because the old man is happy when he is dreaming of lions, and whether he regains the strength to return to his beloved pursuits or not, his spirit remains indomitable.
Santiago tells the boy in the first 15-20 pages, "when I was your age I was before the mast on a square rigged ship that ran to Africa and I have seen the lions on the beaches in the evening" a couple pages later Hemingway describes the old man as sleeping and dreaming not of the things he used to as a young man like storms, women, nor of great occurences, nor of great fish, nor fights, nor contests of strenth nor his wife, he "Only dreamed of places now and of the Lions on the Beach. They played like young cats in the dusk and he loved them as he loved the boy. He never dreamed about the boy." In the last line of the novel the old man was dreaming of youth. The boy was watching him dream of youth, and santiago had just fought the fish as if he still had his youth, but in the end it was worth no more than a dream.