Paragus is the father of Broly, the Legendary Super Saiyan.
King Vegeta, due to Broly's high power level at birth, ordered his men to kill the infant. Paragus tried to convince King Vegeta not to kill Broly, stating that he would grow up to be a great warrior, but failed.
In Universe 3, after Baddack battled King Vegeta for the throne and won, Broly was spared and Paragus thanked Baddack. Paragus is not seen again after this and is presumed dead, since it appears that Raichi killed all Saiyans in this universe except Baddack.