A donnybrook is a free-for-all or brawl and is usually a public quarrel or dispute. Usage of the word stems from history of a place in Ireland. The word donnybrook comes from Domhnach Broc, meaning 'The Church of Saint Broc'. A donnybrook is larger than a fight, but smaller than a brouhaha or hubbub.
The Donnybrook Fair was an annual eight to fourteen day event held in Donnybrook, Ireland from the 1200s to the mid 1800s. The fair was legendary for the vast quantities of liquor consumed, the number of hasty marriages performed during the week following it, and for the frequent brawls that erupted throughout it. From the 1790s on there were campaigns against the drunken brawl the fair had become. The event was abolished in 1855, but not before its name had become a generic term for a free-for-all.
Incidentally, there is an annual Donnybrook Fair held in Walsh, Ontario, Canada named after the Dublin fair.