The movie, and the book, Life of Pi tells the story of a boy named Pi and his battle for survival while aboard a life boat.  The story begins in Pondicherry, and readers/viewers see into Pi's life.  He is an incredibly curious and tolerant boy.  He sees no reason why he can't practice three religions at the same time.  His family is in charge of the city zoo, so Pi learns a great deal about animals during his childhood.  Unfortunately, Pi and his family must leave Pondicherry.  They board a freighter with many of the zoo animals and leave to go to Canada.  The ship winds up sinking, and Pi is fortunate enough to make it into a life boat.  He is the only human in the life boat.  The other passenger is a tiger named Richard Parker.  The rest of the story is about how Pi and Parker survive together on the life boat for weeks on end.  

The psychological aspect of the story is squarely focused on Pi's struggle to not give into fear and hopelessness.  His situation is dire, and it would be easy for him to just give up.  But every day, Pi finds enough inner strength to keep on trying to survive just one more day and keep Richard Parker alive as well.