An answer as to what the tiger represents will vary according to an individual's reading of Life of Pi. Some readers, for instance, will feel that the tiger represents fear. Others may believe that it is a symbol of unrestrained animal nature. In the latter case, it is ironic that the tiger is given the prosaic name of Richard Parker, which suggests an everyday man from an English-speaking country.
One answer which combines well with both the above, as well as many other responses to the book, is that the tiger represents Pi's unconscious mind. In this case, one might say that it is Pi's elemental fear that is symbolized by the tiger. The unconscious is the unrestrained, animal side of the mind, and Pi is forced to allow this side of his mind free rein when he is away from the comfort and protection of civilization. He must do what is necessary to survive, including killing anyone who is a threat to him.
In the third part of the book, Pi tells an alternative story, in which he kills and eats the murderous chef who has killed his mother. The investigators note that Pi plays a similar role in this story to the one Richard Parker plays in the first, giving further weight to the idea that the tiger represents Pi's unconscious mind, the part of the human that is purely animal.