"He has thought of nothing but his soft bed and his warm hearth ever since oh god he's behind me isn't he?"
Everyone but Thorin is thrilled to see Bilbo, and they ask him how he managed to get past the goblins. Bilbo avoids the question; Gandalf gives him an odd look, but says it doesn't matter. Thorin presses the issue: he wants to know why Bilbo came back. Bilbo Baggins concedes that he has thought of the Shire often, and he truly does miss his home. He's come to better understand what Thorin's Company must feel regarding Erebor, and pledges that he will do his best to help them reclaim their homeland. Moved, the dwarves all look on the hobbit with a newfound respect.
The Book: Bilbo, lost and still wearing the ring, wanders around a valley on the other side of the mountains. He hears voices, and creeps into a dell where the dwarves are encamped. Balin is the look-out, but cannot see the invisible hobbit. Gandalf and the dwarves are arguing about Bilbo; the wizard wants to go back and look for him, but the dwarves (the book does not mention which ones) argue that he's been more trouble than use. They blame Dori for dropping him. When he starts to defend himself, Bilbo slips off the ring and surprises them all. They are amazed that he managed to sneak by Balin, and ask him where he'd gone. He tells them the story, including Gollum and the game of riddles, but decides to leave out the part about the ring. Bilbo's story about dodging goblins, tricking Gollum, and sneaking past Balin wins him a new respect with the dwarves. Gandalf gives Bilbo an odd look, but then tells their side of events. After everybody is all caught up, Gandalf gives the order for everyone to move on. Bilbo complains of hunger, but since their rations are with the ponies (which the goblins still have), there's nothing to do but snack on some berries during their march.
What difference does it make? This is an enormous difference. The book version of Bilbo Baggins gains the respect of the dwarves through his deeds - he sneaks past their best look-out, and tells an exciting tale of adventure in the mountains. Furthermore, Thorin has no strong feelings towards the hobbit at this point in the novel; his mild irritation at Bilbo Baggins is shared with the rest of the dwarves. In the movie, there isn't really enough time to swap stories, and nobody seems to care that he snuck up on them. The movie also revisits Thorin's disdain for Bilbo as a lodestone, and has Bilbo win the dwarves respect with a moving speech.
My Opinion: This was amazing.
It's not like I ever had a problem with the book's version of events. But this scene is a payoff to a lot of little things that Peter Jackson had been building up, almost independently of the novel's narrative: namely, Thorin's lack of respect for the hobbit, and the dwarves' quest to retake their homeland. In the book, the focus of the dwarves' quest is on the gold. The movie makes it pretty clear that they want their home back. Their goals are loftier and more noble. The movie also greatly emphasizes Thorin's disdain for Bilbo. These are both things that technically are in the book, but they're so lightly touched upon that they're almost insignificant details. The movie plays them up so much more.
It's a good thing, too, because that gives us this scene. Bilbo Baggins is given a reason to help the dwarves that is simply not present in the book, where he just decides to go on an adventure for no real reason. This not only creates a stronger sense of nobility in the hobbit, but is still entirely in character. Peter Jackson has taken Bilbo's love for his home, a source of comedy in the books, and turned it into an altruistic motivation. This is a big change, but it is an excellent one.
"Yeah I'm pretty much the shit. No big deal, though."