What does bilbo take from the hoard?

Bilbo takes the Arkenstone from Smaug's hoard.  In chapter 13, after Smaug has left the mountain and his treasure to terrorize the men of Lake-town, the dwarves and Bilbo are locked inside the mountain.  The dwarves see Bilbo reach down for something from the treasure pile he is standing on.  They don't know it, but Bilbo has found the Arkenstone.  Thorin had described it and Bilbo knew how much it meant to Thorin.  Bilbo isn't exactly sure why he's taken it, but instinctively seems to know that it will prove useful.  Later, it does prove useful when Bilbo uses it as a bargaining chip to bring about peace between the dwarves and the men and elves - all who want part of the dragon's treasure (chapter 16).  Bilbo's attempts to bring peace fail, however, and Thorin turns against Bilbo despite the Arkenstone (chapter 17).