Bergelmir was the frost giant grandson of Ymir, the first frost giant, who along with his wife were the only giant survivors of the enormous deluge of blood which flowed from Ymir's wounds when he was killed by Odin and his brothers Vili and Vé. According to the Gylfaginning, the two escaped the flood of blood and subsequently became the progenitors of a new race of frost giants.
They sailed for weeks until they found new land. Bergelmir called it "Jötunheim", a realm where the Giants served no master but themselves. Bergelmir and his wife proceeded to repopulate their race and ruled benevolently over the Giants as King and Queen.
Bergelmir never sought vengeance against Odin for the murder of Ymir or the near-extinction of his race and chose to prosper instead. He eventually died of old age, surrounded by people who loved him.