put a fork in it

It means you’re done. Just give up. It’s over. No going back.

“Put a fork in it, you’re done.” David Spade, SNL Weekend Update; in reference to actor Erik Estrada’s career.

she put the fork down

Meaning she starved herself.

Girl : “I wonder how she got her body so beautiful and slim.”
Man : “Haha, I know why!”
Girl : “Why?”
Man : “She put the fork down!”