The Rains of Destruction was the event in which much of the world was destroyed, involving thousands of Moon Stones from each of the 6 Moons falling on the lands of the world, destroying everything on them with the impact.
Later in the game, the player finds out the Rains can be called down by Zelos, the Silver Gigas, and were originally used by the Silvites, who deemed that the other civilizations were not worthy of continuation due to their constant fighting over territory and violent use of Gigas.
Ironically, it is the Rains of Destruction that allowed for new civilizations to be created, as natural resources (Moon Stones) were now replenished by the Rains.
Unknowingly, Fina's quest revolves around the Rains, as the Silvite Elders wish to use them again on the world in order to cleanse what they see as impurities. However, soon after this is discovered, Galcian steals the Moon Crystals and raises Soltis, using the Rains of Destruction on Valua. They then become the main threat of the game, as Vyse and his group attempt to stop them being used again. After the death of Galcian, Ramirez attempts to use Zelos to destroy the entire world, but is stopped when the Great Silver Shrine crashes down through the beam and into Soltis, allowing the party entry.
After the destruction of Ramirez and Zelos, the Rains of Destruction are no longer a threat as Zelos was the only being with enough power to call them.