What are some major differences between the book Divergent and the movie? Why is this significant?

Generally, the movie is less focused on visual violence, and there is less emphasis on the romance between Four and Tris. As the movie is rated PG-13, the director, Neil Burger, opted to highlight the terror of Roth's dystopian world on a more psychological level. For example, Edward's eye-stabbing incident is completely left out of the movie; in the book, the sheer violence associated with Edward's ordeal reinforces the horrors associated with Dauntless training. Also, Al, Peter, and Drew's attack on Tris is significantly toned down in the movie; Tris’s sexual assault is never portrayed on screen. Additionally, the three Candor foes (Peter, Drew, and Molly) are significantly less belligerent in the movie, both on a physical and emotional level. On screen, Molly congratulates Tris after her courageous stand for Al, a gesture that would be foreign to the Molly in the book.
While the actions of the book’s antagonists reinforce the visceral brutality of Roth's dystopian world, the movie focuses on the psychological dimensions of fear, entrenched social divisions, and the classic hero's journey. Neil Burger brings the fear landscapes to life on screen, giving us an intimate glimpse of Divergent's Kafkaesque world. The visual stimuli is stunning and extremely effective. Meanwhile, Tris and Tobias’s romance is less apparent in the movie than in the book. Again, this may be due to the movie's PG-13 rating: there is only one prolonged kiss in the movie compared to numerous kisses in the novel. On a more significant level, the final screen fight between Tris and Jeanine is a nod to modern sensibilities and expectations. Tris defeats Jeanine in a decisive physical battle, satisfying our appetite for on-screen justice. In the book, Tobias is the one who shuts down the simulation program. In the movie, however, Tris plunges a knife into Jeanine's hand and a syringe full of simulation serum into Jeanine’s neck, forcing Jeanine to shut down the malevolent simulation program. When Jeanine awakens from her stupor (and realizes what she has done), she attacks Tris. However, the Erudite leader is no match for the stronger and faster Tris. Here, the artistic license taken by the director reinforces the depth and scope of our heroine's victory over evil.