Din's Fire
Din's Fire is Zelda's Side Special Move in Melee and Brawl. It is an attack with considerable range, and when it hits your opponent, it sets them on fire and knocks them upward. It can be controlled with the control stick (while holding B) and can be released by letting go of the B button. The longer the B button is held, the stronger the attack. When done in the air, it sends the user into the helpless state. It can be countered or deflected, but this will not send the projectile back at the user. It can also be absorbed by Ness' and Lucas' PSI Magnet and Mr. Game & Watch's bucket.
Due to the long wind-up and wind-down lag of this attack, the key to its successful use is prediction and precise timing. It is mostly used to prevent opponents from rushing in at Zelda or as an edgeguarding technique.
If an opponent were to hit Zelda while this projectile hasn't exploded yet, it will still continue going as if the move were being charged but Zelda doesn't have control of it anymore. Also it is still dangerous once it does explode, even out of Zelda's control.
Zelda's Din's Fire in Brawl appears to function similarly, but moves and detonates much faster, has less lag, has a larger hitbox, and deals more damage and knockback, making it a somewhat more legitimate projectile, though it is easy to dodge in high level play. Multiple hits can be juggled on an off-the-stage opponent, and at around 150%, it can Star KO an airborne opponent. This move is more effective against CPU's than against human players, as they tend to make less of an attempt to dodge it.
It should also be noted that Zelda travels straight forward horizontally if she uses it in the air, allowing it to be used as a Guard Break.
Origin
It is based on the Din's Fire spell from The Legend of Zelda: Ocarina of Time. Although, rather than being a small sphere, it is a large explosion of fire radiating outwards from Link, used primarily as an offensive spell, but also used to solve puzzles. It is the spell which is representative of Din, the Goddess of Power.