Din's Fire is a magic spell that appears in The Legend of Zelda: Ocarina of Time. It is obtained from the Great Fairy of Magic in a cave near Hyrule Castle. Once Link has obtained bombs from Death Mountain, he can blow open the entrance to the cave and talk to the Great Fairy inside. While the other two magical abilities in the game, Nayru's Love and Farore's Wind, are used for defense and travel respectively, Din's Fire is an offensive spell used to attack enemies. Once cast, Link will toss a ball of fire at the ground which expands and surrounds him dramatically harming enemies in the radius. Of the three magic spells, Din's Fire is the only one that isn't optional as it's required for lighting a ring of torches to enter the Shadow Temple.
Super Smash Bros. Series
Princess Zelda can use Din's Fire as a special attack in the Super Smash Bros. series, debuting in Super Smash Bros. Melee and returning in all later installments. The move is Zelda's side B move, which when executed will cause Zelda to release a ball of flames. You'll be capable of controlling where it goes, though not entirely. Once the ball is close enough to one of your opponents, you'll be able to press B to make it explode.
Originally Din's Fire was going to be a spell that Link received after obtaining the Fire Medallion and would have been cast by using the medallion as an item. This is why the game says that Darunia "adds his power to yours!" after he gives you the medallion.