I was thinking about your question and couldn't come up with an answer. Asked a few people and they couldn't remember. The only number I know the meaning of is "187" that you hear in some songs these days, which means officer down. Don't know why THAT popped into my head.
Ill ask around but I think Cape Chef or Athenaeus may know the answer. Maybe it was a military term?
I have heard different stories for this, but the one I hear the most often has to do with Delmonico's in NYC (the original). Supposedly, they had 85 items on the menu, thus no item numbered 86 so that was the number used to designate items that had been sold out. I have no idea how true this story is, but as I said this is the one I have heard the most often.
There is already a thread on this topic in the archives. I think my response was; the term 86 came about because the garbage can in the army was a diamiter of 86 inches. So to 86 something is to throw it out.
If I remember right there were a few other answers.
It's 8:45 on a busy Friday night. The saute guy realizes he just took the last veal special out of the saute box to start it for table 18. He sings out, to everyone in general, "86 the veal special!" A groan comes out of the collective wait staff. This is the third Friday in a row those albanian dummies have run out early. Now they all have to explain to the salivating hordes, who are already annoyed because the air conditioning is broken and the mandatory water ban means they have to ask for water, that the veal special is gone for the night.
You keep a chalkboard just inside or outside the kitchen, where the waiters (but not the customers) can see it. The board is labeled: 86s. On it you list the regular items that you should have, but don't. To stop the waiters from taking orders for them. Of course, you still have to tell the waiters repeatedly, because you cannot assume they know how to read. (Not necessarily my opinion, but sometimes true, alas.)