It means that the restaurant has run out of a particular item. So if someone says, "86 Sea bass!", that means the last order of sea bass has been spoken for.
There have been many stories about the origin of the term, the most common that I've heard was that there was this particular restaurant (I THINK it was in NYC) which listed their most popular menu item as #86. Because this item was constantly being sold out, the term 86'd sprung from that.
Now you hear it used in other contexts, like if someone got fired.
"Boldness has genius, power, and magic in it."
Johann Wolfgang Von Goethe