A Troll Purse was a strange creature of unknown origin that Trolls use to avoid being pick-pocketed. Bilbo Baggins encountered one that belonged to the Stone-troll, William, in The Hobbit. The same one is featured briefly in the Hobbit Game Cube game.
When Bilbo was sent by Thorin to steal something from the Troll Camp; Bilbo snuck up behind William and took his purse, but the purse yelled and alerted William, getting Bilbo caught. It is unknown what happened to the purse after its owner was turned to stone.
It is unknown what these creatures are or where they came from. They couldn't have been made by Trolls (Trolls can't make much of anything) as even Morgoth can only alter (not truly create) life. They could have been bred by Sauron for the purpose of making sure that important goods carried by trolls could not be stolen. However (since it would be strange to create such a being just for trolls); it is likely that they go all the way back to the First Age, bred by Morgoth to resemble purses. In this case, they were probably used by spies and thieves.
If one of the pre-mentioned possibilities is correct, then trolls probably took these "purses' for themselves after the fall of Sauron at the end of the Second Age. Either trolls figured out how to breed them; or the purses live forever and were antiques among trolls (unlikely). Apart from the pre-mentioned, the only other possibilities are; they are creatures that have an uncanny resemblance to purses, or they were animals of some sort decorated to look like purses. It is unknown whether trolls actually keep their valuables in the troll purses; or if they keep their valuables else-where and the troll purse is just a lure. If the latter is the case; then the fourth and fifth possibilities are more likely than the first three (and vica versa).
Given that when Bilbo took the troll purse from WIlliam's pocket it yelled; "Oi! Who are you?", we can either assume that troll purses are sentient, or are trained to respond in certain ways.