A sword that can kill an immortal god. The emperor Soniel attempts to kill Fou-Lu with it, though this fails for unknown reasons (possibly because he was too powerful, or because because he was only half a god). After Fou-Lu beheads Soniel (deleted in the European and North American versions as it was considered too violent - however, the scene from the Japanese version can be viewed here, from around two and a half minutes in) Yuna then takes the sword. However, Ryu later takes it from him, and Cray uses it to end Elina's suffering, as she has been changed into an Endless.
Though the information is not inside the game, the official source book explains that the Dragon Slayer was originally a god, another Endless that had been summoned incorrectly by Yuna. In this case, only the head of the god appeared, and Yuna decided to crush it and forge it into a sword. However, the god's hatred and desire to find its body remained inside it, and it tries to absorb the abilities of any god like itself to gain more power, presumably making them mortal, which presumably makes them liable to be killed by the blade itself.