What is Dangling A Carrot Will Entice A Horse To Run?

It refers to the idea of sitting on the back of a horse with a carrot attached to a stick by a string, almost exactly like a fishing pole, and dangling the carrot out in front of the horse. The horse would move forward in an attempt to eat the carrot, but in moving forward it would move you and the carrot forward as well. So, the horse will never be able to reach it no matter how fast it runs.

It is a way of saying that you will get those under your control to work harder if you show them a reward and insinuate that they will receive it if they work hard enough. Sometimes this practice is seen as manipulative, as there may be no actual intention to pay out the reward.