Casual racism shouldn't come so easily to you, Bilbo Baggins. You've been hanging out with Thorin too much.
Bofur is offended, but he warmly offers Bilbo the best of luck and lets him go. However, before the hobbit can take off, they see his sword glowing blue. Bofur is confused, but Bilbo knows exactly what it means: goblins are nearby.
The Book: No such scene occurs. Gandalf tells Gloin and Oin that they cannot light a fire, but the dwarves are otherwise in high spirits for the night. They tell stories, discuss what each would do with their share of the treasure, and blow smoke rings, which Gandalf turns into different colors and dances around the roof to amuse everyone else. Bilbo Baggins falls asleep with the rest of them.
What differences does it make? This is an enormous change to the novel, and in fact the culmination of several other smaller changes. From Bilbo's screw up with the trolls to his near death on the cliffs, Peter Jackson has constantly and consistently downplayed Bilbo's worth to the dwarves, instead portraying him as a worthless lodestone. The payoff for these small changes is here. In the novel, Bilbo does not have much of a reason to want to abandon Thorin's Company, aside from missing his home. Though he occasionally grumbles about how much he misses his chair or kettle, Bilbo never struggled to justify his decision to leave home. Peter Jackson's version of the character does, and it is such a difficult internal struggle, that Bilbo Baggins actually decides to skulk away from the dwarves in the middle of the night. This changes the character of Bilbo Baggins, and introduces a personal conflict that is not present in the novel.
My Opinion: I can see a lot of people getting upset with this change - it's nearly as bad as Frodo sending Sam away in Peter Jackson's Return of the King - but I honestly quite like it. It portrays Bilbo Baggins as a little more conflicted (and therefore interesting) about his decision to leave home, and makes the decision look bigger than it may have otherwise. He's realizing, after being attacked by orcs and trolls, that he might not be cut out for the adventuring life. This allows him (and us, the audience) to be surprised by his later bravery, and to see character growth that simply isn't present in Tolkien's novel.