to be finished with or tired of, your current activity or situation.
It was 1980 or 81, when I was working for a bank on Long Island, that I said this to my co-worker Bill. The office dress code back then was suit and tie. For fun, I used a plastic fork to secure my tie to my shirt. The real meaning behind this was to indicate that I was tired of the long hours on my current job, and had decided it was time to get a different one, thus Stick a fork in me, I'm done.