There are many symbols used in the course of telling Santiago's story. Santiago himself could be seen as one symbol, a representative of the human spirit that maintains its pride and dignity despite hardships and the decline in ability that comes with old age.
The memories of Africa and especially the dreams of the lions are symbolic of his youth, the days when he was free and capable of controlling his destiny, and of his dream of returning to those carefree days.
The sea represents everything that challenges any person in life. It provides his livelihood, reveals beauty and danger, challenges him to great exertion but also rewards him with the great catch of his lifetime. In the end, however, the old man needs to struggle on, alone and disappointed but never defeated.