The tiger symbolises wildness and strength. He also represents the brutality of nature. Richard Parker's needs must be met to maintain order and balance. The tiger is also symbolic of Pi and is in fact meant to represent Pi's own nature which embarrasses him by its carnality and beastliness. To keep the tiger happy means to keep himself alive.
The hyena symbolises evil. While it could be on the same side of brutality as the tiger, it is characterized as being recklessly brutal and mean. It will eat any and everything - whereas the tiger eats out of necessity, the hyena will go to selfish lengths to ensure that he does not starve. In the story, they hyena is understood to be the human survivor the French cook.
The orangutan symbolizes comfort and security - she is protective and motherly and can be understood as Pi's mother.
Lastly, the zebra represents weakness and frailty. The zebra is wounded and unable to help himself. In the story he represents the Chinese shipmate who is eaten first.