Falchion is a sword of legend in the Fire Emblem titles set on Archanea. Originally created by Naga from one of her own fangs, it eventually found its way into the possession of the hero Anri, who used it to slay Medeus. It was then passed down through generations of the Altean royal family. Lost after Marth's father was killed in battle, Marth himself later reclaims the weapon and uses it to stop the ambitions of Gharnef and a revived Medeus.
Thousands of years later, long after the nations of old faded into history, Falchion is wielded by Chrom, a distant descendent of Marth, in Fire Emblem: Awakening. The sword is also wielded by Chrom's daughter Lucina, who travels back in time to aid him. Chrom, who is of exalted blood, performs a ritual late in the game called the Awakening and asks that Naga unseal the full potential of the Falchion, which he then wields in the final battle against Grima.
Fire Emblem Gaiden
In Fire Emblem Gaiden, Alm is also able to wield Falchion, though this is not the same weapon as the one handed down through Marth's bloodline. It is a different sword, and it houses the spirit of the imprisoned goddess Mila.