The Goron Bracelet is an item Link will come in possession of in The Legend of Zelda: Ocarina of Time as a young child. He'll use it to pick up Bomb Flowers, which were previously too heavy for him to lift. Oddly, this is its only purpose, and as an adult Link will no longer need them.
How to get
Darunia is in a depression and you must lift his spirits by playing Saria's Song on your Ocarina in Death Mountain. Doing so will cause him to rejoice and start dancing. Following this he'll hand over the bracelet, which will allow the player to gain access to Dodongo's Cavern.