A blood feud was a conflict between social groups, often families, that resulted in a cycle of retaliatory violence.
Until the 2260s, Acamarian society was plagued by blood feuds between rival clans, in which the slightest injury to a clan member demanded violent retribution. These feuds could last decades or even centuries, passing from generation to generation, and plunged Acamar III into chaos. (TNG: "The Vengeance Factor")
Blood feuds were common between the Great Houses of the Klingon Empire. Whenever a Klingon was killed or dishonored, the other members of their House were obligated to seek vengeance. Jadzia Dax jokingly remarked in 2374 that this state of affairs was "boring". (DS9: "Sons and Daughters")