Definition:
The Carrot and Stick Approach of Motivation is a traditional motivation theory that asserts, in motivating people to elicit desired behaviors, sometimes the rewards are given in the form of money, promotion, and any other financial or non-financial benefits and sometimes the punishments are exerted to push an individual towards the desired behavior.
The Carrot and Stick approach of motivation is based on the principles of reinforcement and is given by a philosopher Jeremy Bentham, during the industrial revolution. This theory is derived from the old story of a donkey, the best way to move him is to put a carrot in front of him and jab him with a stick from behind. The carrot is a reward for moving while the stick is the punishment for not moving and hence making him move forcefully.
Further Reading:
Book: Agile Competitors and Virtual Organization by Steven L. Goldman, Roger N. Nagel and Kenneth Preiss