The legend: brother of Kahless
According to Klingon legend, Morath dishonored himself as well as his family by telling a lie. Kahless challenged Morath and told him to repent for his dishonorable act. Instead, Morath fled, and was pursued by Kahless across valleys and mountains to the edge of the sea. With no place left to run, Morath was forced to fight Kahless for twelve days and twelve nights, until Morath was killed. (TNG episode: "New Ground") Despite the dishonor Morath brought on the family, Kahless then attempted to redeem his brother by descending into the depths of Gre'thor, and to guide his brother to Sto-vo-kor. (VOY episode: "Barge of the Dead")
The legend of Morath and Kahless is considered an important tale in Klingon culture. The fight between Kahless and Morath was depicted in sculptures owned by both Worf (TNG episode: "New Ground") and by Koloth (TOS novel: In the Name of Honor)
The man: son of Ondagh
The legend of Morath, however, was significantly different from historical fact. Morath was in fact an only child, the son of Ondagh. His birth was a difficult one for his mother, and Ondagh prayed to the Old Gods of Klingon legend to spare her life, in return for his eternal gratitude. She did not survive, causing Ondagh to curse the name of the gods, and inspiring in him a hatred of anyone that told a lie. One day, when Morath was young, he told a lie, sending Ondagh into a rage. Ondagh beat his son, nearly killing him in order to teach him a lesson.
Sometime later, marauders attacked Morath's village. Morath cowered in fear while Ondagh was left alone to fight the intruders alone, and despite stopping several marauders, Ondagh was killed. Morath left the village in grief, and as penance, decided to take the ideals of his father and ensure that the truth was always upheld.