The slang term “bun fight” is used to refer to a formal event which requires people to dress up, whether or not the event features food, let alone buns. You may also hear it used in reference to a large party at which food is served, and a bun fight may also appear in the guise of a petty argument. In any case, the term appears to be British in origin, and it appears on occasion in British novels and newspapers, so it can be handy to know what it means.
The roots of this term are a subject of debate. Some people link it with famous comic author P.G. Wodehouse, while others believe that the term is actually a bit too old for Wodehouse, emerging in the later part of the 19th century, when Wodehouse was still quite young. In any case, this slang term is widely used by authors who try to write in the style of Wodehouse, perhaps in homage, and it also appears in perfectly respectable publications, such as the Times of London.
If you hear the term “bun fight” and you think of people whipping pastries around, this isn't far from the idea. Originally, the term appears to have arisen in reference to formal teas and dinners given by high ranking members of Victorian society, and it was meant to be tongue in cheek, as of course no food would be thrown at these events. Over time, a bun fight, or bunfight, came more generally to mean any kind of formal event, often with an implication of very stiff, formal behavior.
Some institutions hold annual bun fights, serving large amounts of food and encouraging members of the organization to dress up and have a bit of fun. Many organizations with a sense of humor identify these annual events explicitly as bun fights, poking fun at formal British culture, while others use more dignified terms. In the news, formal events of note are sometimes referred to as bunfights by insolent reporters who wish to make light of such events and the people who attend them.
You may also hear someone refer to a petty argument as a bun fight, referencing a fight between nursery school children over food in the school yard or nursery. The slang term is usually used in this sense by outside observers who wish to point out that the argument in question is a bit absurd and overblown.