Increases chance of receiving drops from enemies.
There are different theories on how it all works and there have been different tests done on the matter over large sample sizes and yet all it does is make people argue about Treasure Hunter.
Treasure Hunter has no effect on quality of loot from treasure chests, coffers or caskets of different kinds. To change that common belief is to put tarutaru inside of a box before opening. See: Shakalaka
Beside Treasure Hunter there have been extra additions made that increase chance of an item drop such as blue !! proc inside Abyssea. This has lead to another batch of conspiracy theories such as this system has always been in the game and that Square only recently has decided to visualize it. There are theories of tarutaru sacrifice affecting the drop rate. Again, see: Shakalaka