There are two common meanings to the phrase ‘Eighty Six’, both of are commonly in context to restaurant slang. The first one means to refuse or reject to serve a customer. The second is used to indicate that an item is finished, and should be taken off the menu.
Example of use: “please inform the staff that the mushroom ravioli is 86. Make sure that they are not mistaken with today’s special fettuccine risotto.”
There are many theories regarding the origin of the phrase, some say that it originated as a slang for the word "nix", that was used in restaurants during the 1930s as a way of saying that the kitchen was out of something. Others say that it originated during the Prohibition era, at Chumley's, a NYC bar. The owner has some policeman on a payroll, and they would call him and worn that a raid was about to happen and he should 86 his customers by making them exit through the back door which was located on 86 Bedford Street.