The answer to this question can be found in the fourth letter that Robert Walton writes home to his sister Margaret, who lives in England.
On July 31st, Walton said, he and the rest of the people on the ship had seen a huge man sitting on a “sledge” with dogs pulling him. They made no contact with this man. But the next morning, they found another man with his dog sled and his one surviving dog. This was the man that they took on board the ship since he was in such bad shape that it was a few days before he could talk. When the man did talk, he was asked why he was so far out on the ice. He said it was “To seek one who fled from me.” On further discussion, it seems that the giant man is the one he is seeking.
So, the man picked up by the ship says he is there pursuing the giant man.