A busted draw is simply a draw hand that didn't come in.
If you flop four cards to a flush or straight, you will frequently have PotOdds to call to the river. If you get to the river and your flush or straight has not materialized, all you have left is a busted draw. You should feel no shame in folding such a hand; it's par for the course.
River bets against a busted draw have no value.
If you make a river bet into someone who was on a draw and they made their draw, they will likely raise back and beat you, for a costly loss. If you bet into them and they are left with a busted draw, they will merely fold. Your only possibilities are a costly loss, and no profit. You can not ValueBet.
If you have no handed either (perhaps you ALSO have a busted draw), you may still stand a chance of stealing the pot by bluffing on the river. For example, say you were on a flush draw, and you suspect your opponent was on a straight draw. The river made neither hand, and you believe your opponent's high-card hand will beat yours. While you can not value bet, you still have a chance of bluffing at the pot and winning, as long as your opponent really is on a busted draw, and not calling you down with a marginal made hand.