"Having a monkey on your back" means you are carrying around a problem or a burden that you don't want. In management terms, monkeys are referred to as problems that can be passed around the office.
Mark Cuban says, "The people who tend to work for me for a long time, they understand that the greatest value you can offer a boss is to reduce their stress." He added, "I never want to get rid of them."
Said another way, the greatest value that you can offer a boss is to take care of your own monkeys and don't dump them on his desk and leave. Here are a few thoughts on how to add value by handling your own monkeys:
1) Cut out the drama. Some people thrive on drama in the work place but this is the exact kind of person that Mark Cuban doesn't want. Less drama, less monkeys for everyone to deal with.
2) Bring solutions, not problems. Handling your own monkeys doesn't mean that you ignore problems or keep them a secret. It simply means that you never raise a problem without a proposed solution.
3) Think about and try to appreciate the pressure that your boss or manager is under. Chances are that they have enough monkeys of their own. Show your appreciation by removing stress from their plate rather than adding to it.
If you want to maximize the value that you offer, make a habit of reducing the stress that others experience. Keep your monkeys to yourself.