A feud is a long-standing fight, often between two families. In Romeo and Juliet, Shakespeare describes the lovers' long-feuding families, the Capulets and the Montagues.
Feuds do not have to be violent—what characterizes them is long-standing hostility. Ethnic groups can sometimes be said to be feuding. Kids in school who refuse to sit at the same lunch table over a period of years could describe their relationship as a feud.