Balmung is the name of King Alric's magical sword, which shoots forth lightning to all adjacent to it when swung.
In Norse mythology, there are legends of a sword called Nothung, or Gram. Gram was the name of the sword that Sigurd (Siegfried) used to kill the dragon Fafnir. It was forged by Weyland The Smith and originally belonged to his father, Sigmund, who received it in the hall of the Volsung after pulling it out of a log into which Odin had stuck it - nobody else could pull it out. The sword was destroyed and reforged at least once. After it was reforged, it clove an anvil in half. See Sigurd for more details on the story of Siegfried and Fafnir.
In the Nibelungenlied, Siegfried's sword is called Balmung.