The Triforce is a magical relic created by the Golden Goddesses, Din, Farore and Nayru. There are three pieces of the Triforce, the "Triforce of Courage" (right) held by Link, the "Triforce of Wisdom" (left) held by Zelda and the "Triforce of Power" (top) held by Ganondorf. In Rose Warriors, it is a major artefact and the focus the "The Rise of Descent" arc.
The Triforce is first mentioned by Zelda to Ruby, Toro and Mario when they initially wake up in Fairy World. Zelda explains that the Triforce is able to grant any wish that the holder(s) ask, regardless if their intentions are good or evil. She says that this power may be able to restore the universe to it's previous state.
Once the Triforce shards, which were scattered throughout the many worlds, are collected, Zelda appears once more to explain that the relic's power is strongest at sunrise. Unbeknownst to them, the Triforce's power becomes too great, stopping time within a 50km radius. A large number of supervillains, headed by Morcubus, then ambush the Rose Warriors, waking Palkia and Dialga from their eternal slumbers. They destroy the Triforce once more, sending the shards back to their original resting spots and restoring time to it's previous state.
Once the Triforce has been reclaimed (again), Ruby wishes that the evils will be no more, which makes the relic explode, killing several people, and sends the supervillains to Abra-catraz in Fairy World, and cleans the Nothing from the Earth.
The Triforce then embeds itself into three powerful individuals, granting them great power.
These three individuals originally held the three Triforce pieces, before the worlds collided, sending the Triforce pieces to various locations throughout the world.
At the end of the game, the Triforce embeds it's power in the hands of these three individuals, granting them immense power.