Stick and carrot, or as I know it, carrot and stick is a notional method of driving a donkey forward, mostly used in jokes and cartoons.
It is based on the donkey's supposed desire to eat the nice juicy carrot. Get a stick, tie a string to the end of it, and dangle a carrot from the string. Sit on the donkeys back and hold the stick up so that the carrot dangles in front of the donkey's eyes. The donkey will supposedly walk forward, like Tantalus, perpetually trying to catch up with the carrot. I have no idea if this really works, but it looks funny anyway.
Another more detailed version has the carrot dangled in front of the donkey, and the rider beating the back of the donkey with another stick, giving the dumb beast something to move away from as well as something to move towards.
By extension, carrot and stick refers metaphorically to incentives, the implication being that both positive reinforcment and negative reinforcement are present - not only will success be rewarded by being given a metaphorical carrot to eat, but failure will also be punished by a metaphorical blow from the stick.
In this metaphor it would seem that the carrot is no longer attached to the stick, nor is it perpetually out of reach. Then again, getting one pay check doesn't stop you wanting the next one, and sufficient funds may still be perpetually just out of reach.
This metaphor is often used in phrases like "x is the carrot, and y is the stick", meaning that x and y are the respective positive and negative incentives of the situation, or my life has no carrot, meaning that negative reinforcement is all that you experience.