Right? It's leg? God, I seriously fucking hope that's its leg they're standing on.
As the three giants fight each other, the Company gets separated. The giants continue to battle, and one manages to kill the other, sending it (along with the dwarves stuck on its leg) crashing into the mountain. Thorin screams in despair, fearing his kin dead, but he rushes forward and sees none of the dwarves injured. Bofur shouts that Bilbo is missing, and they quickly find him dangling precariously over the side of the cliff. Ori and Bofur try to help, but cannot reach the hobbit; Thorin has to leap down to rescue him. Dwalin, who pulls Thorin up, is happy that they haven't lost their burglar. Thorin says scornfully, "He's been lost ever since he left home...he has no place amongst us" and leads the Company into a nearby cave.
The Book: One rainy dark night, Bilbo and the dwarves (and Gandalf) find shelter under a hanging rock. They watch in awe as, across the valley, stone giants are tossing rocks at each other for a game. The giants are far away, and playing instead of fighting (Bilbo can hear their laughter and shouting echo throughout the mountains). Thorin complains that the shelter they have is inadequate. They send Fili and Kili to scout out for something better, who come back very quickly, having found a cave. Gandalf, fearing that the caves may not be unoccupied, asks them if it had been examined thoroughly. They insist that it was, though none of the Company believes them.
What difference does it make? The big change here is the behavior of the giants. In the book, they are harmlessly throwing rocks at one another, a great distance away, and pose no threat to the dwarves (though Thorin does fear that they risk being used as "footballs" by the giants if they don't find better shelter). The movie bring them closer, and makes them far more dangerous; the dwarves are caught in the middle of an enormous brawl. Bilbo does not fall, and consequently, he is not insulted by Thorin for being a worthless addition to his group.
He just happens to really hate it when people fall.
My Opinion: This is such a small change, that makes such a great spectacle. It really doesn't matter if the stone giants were a threat or not; the way Peter Jackson portrays them is a bit gratuitous, but it doesn't really change anything of value. The scene adds a lot of excitement, and it does so without affecting the rest of the story. The big difference is the short exchange between Thorin and Bilbo at the end of the scene. This level of animosity and disdain was never mentioned in the novel. Your mileage may vary here, but personally, I really like the relationship between the two. It's a good setup for some character development for both of them.
Also, in the book, the narrator refers to the storm that's befallen the dwarves as the phenomenon when one thunder storm collides with another, or, "a thunder battle." When Balin comments that the fighting giants is a "thunder battle," it may not make much sense, but it's a neat little reference to the novel.