The Right of Vengeance is a traditional Klingon matter of honor that is claimed when a Klingon seeks revenge against another.
In 2367, after Duras had killed K'Ehleyr, Lieutenant Worf claimed Right of Vengance against Duras and killed him in hand-to-hand combat. (TNG: "Reunion")
In early 2368, when it was discovered that the House of Duras had conspired to destroy the honor of the Mogh, Chancellor Gowron offered Worf, the life of Toral, in exchange for his family's misdeeds against the House of Mogh. Worf declined because Toral was a boy who had done nothing, a decision he would regret a few years later. (TNG: "Redemption, Part II")
According to Kor, "A Klingon who denies himself the Right of Vengeance is no Klingon at all." (DS9: "The Sword of Kahless")