In the cosmology of Final Fantasy XIV, the 14 worlds are the result of a cataclysmic event known as the Sundering.
To understand the 14 Reflections, you have to look back to the time before recorded history, to the original, undivided star known as Etheirys.
Etheirys was a sprawling, magically rich planet inhabited by a race of virtually immortal, god-like beings known as the Ancients. When an apocalyptic event known as the "Final Days" threatened to destroy Etheirys, the Ancients sacrificed half of their surviving population to summon Zodiark, a primal of immense power, to rewrite the laws of reality and save the star.
However, a dissenting faction feared Zodiark's power and the cycle of sacrifice required to sustain him. Led by Venat, they summoned a counterpart primal: Hydaelyn.
Hydaelyn and Zodiark clashed. Hydaelyn's inherent power was to "enervate" or divide. She struck Zodiark with a blow so powerful that it split not only him, but the entire planet and everyone on it.
Etheirys was fractured into 14 separate dimensions that exist in the exact same physical space but are separated by a dimensional rift. The original world became known as The Source, while the other 13 became parallel worlds known as the Reflections (or Shards). Every soul on the planet was also split into 14 fragments, continuously reincarnating across the different dimensions with only a fraction of their original power.
The antagonists of the overarching story, the Ascians, were the few Ancients who escaped the Sundering. Their ultimate goal was to break down the barriers between the dimensions, merging the 13 Reflections back into the Source to resurrect Zodiark and restore their lost world.
This process is called a Rejoining. To achieve it, the Ascians must push a Reflection to the absolute brink of destruction by flooding it with a specific elemental energy. Simultaneously, they must orchestrate a massive disaster of the same element on the Source. When the barrier cracks, the hyper-charged aether from the Reflection rushes into the Source, completely destroying the Reflection and triggering an apocalyptic "Umbral Calamity" on the Source.
Over millennia, the Ascians succeeded in destroying exactly half of the worlds, while the others remain in various states of survival or ruin.
The prime dimension and the main setting of the game. It is the "center" of the universe. Because it has absorbed seven of the thirteen Reflections, the souls of the inhabitants on the Source are significantly denser and stronger than those of the people living on the remaining Shards. It has survived seven Umbral Calamities.
The Ascians successfully triggered seven Rejoinings. Each of these Reflections was completely obliterated, their aether absorbed into the Source to fuel a Calamity.
The Fifth (Wind Calamity)
The Twelfth (Lightning Calamity)
The Second (Fire Calamity)
The Third (Earth Calamity)
The Sixth (Ice Calamity)
The Tenth (Water Calamity)
The Seventh (Darkness/Astral Calamity - The Fall of Dalamud and Bahamut's rampage)
The Ascians' very first attempt at a Rejoining, and a catastrophic failure. Led by the Ascian Igeyorhm, they flooded the Thirteenth Reflection with Darkness. However, because they did not prepare a corresponding calamity on the Source to absorb the energy, the world's aether simply collapsed. The Thirteenth became The Void—an empty, ruined realm of perpetual darkness. Its inhabitants were corrupted into immortal, aether-starved monsters known as Voidsent. Because it was ruined rather than Rejoined, the Ascians considered it a lost cause.
The setting of the Shadowbringers expansion. The Ascians attempted to rejoin the First by flooding it with Light. It was pushed to the absolute edge of destruction, nearly becoming a "Void of Light." If it had succeeded, it would have triggered the Eighth Umbral Calamity (the Black Rose chemical weapon) on the Source. The Warrior of Light travels across the dimensional rift to the First, halts the flood of Light, and saves the world from being Rejoined. It currently survives as a recovering, intact Reflection.
These four Reflections have not been Rejoined and continue to exist in the dimensional rift. For much of the game's history, they remained completely untouched by the narrative. However, recent lore in the Dawntrail expansion reveals that the high-tech, electrope-powered realm of Alexandria originates from one of these surviving Reflections (heavily implied to be the Ninth). Alexandria's home shard suffered a localized, world-ending lightning catastrophe, forcing its people to bridge the dimensional rift to survive. The remaining three shards are still entirely unexplored.