In the film The Hobbit, after the dragon Smaug is dead, Thranduil comes with some elves to Erebor and wants his heirlooms, the white gems of Lasgalen, back.
Why do the dwarves have these in the first place?
The white gems were given to the dwarves so that the dwarwen jewelers could set them into a necklace.
In the extended edition of The Hobbit: An Unexpected Journey the prologue is a little longer than in the theatrical edition:
All would pay homage to him, even the great elven king, Thranduil.
As the great wealth of the dwarves grew, their store of goodwill ran thin.
No one knows exactly what began the rift. The elves say the dwarves stole their treasure. The dwarves tell another tale. They say the elf king refused to give them their rightful pay.
It is sad, Frodo, how old alliances can be broken, how friendships between people can be lost … and for what?
So, just as told in the book, there was a deal between the elves and the dwarves concerning the fashioning of some jewellery; the deal was not honoured by one side or the other (from Thorin's surprised look at Thror, I'm inclined to believe the elves' version), and as a result the gems were kept by the dwarves.
The difference from the book is that, instead of some generic "gold and silver", the deal is about a specific and well-recognizable piece of jewellery (with a characteristic musical theme playing every time the gems are mentioned), so that it's easier for the viewer to remember them.