A desk banana is a banana that you bring to an office job with the intention of eating, but instead leave on your desk until it overripens and is tossed. The banana becomes a symbol of your failure to follow through with better eating habits.
Person 1: "That banana has been on your desk all day. Aren't you going to eat it?"
Person 2: "Nah, it's just a desk banana. You want it? If not, I'm probably gunna toss it."