It's a metaphor. I've heard "Die on the vine" also. Wither means to dry up or rot. Think about a plant like a grape. The grape is growing on the vine but that doesn't mean it will not be wasted if no one picks it at the right time. An idea or project which is "Ready" but is not taken advantage of withers on the vine. It's no longer possible because the right time has passed.

An opportunity that passed you by. Example sentences: "Don't let this wither on the vine! Act now!" or "Too bad I didn't ask Jesse on a date when he was single. I really let that wither on the vine."