Here is the definition I like by Idealist Careers “In a nutshell, most career experts agree that managing up is a method of career development that’s based on consciously working for the mutual benefit of yourself and your boss. It doesn’t mean avoiding work, rebelling, kissing up, or trying to turn the tables on a higher-up, but instead understanding your boss’s position and requirements and making yourself known as a stellar employee by exceeding her expectations and needs.” I also think managing up is if you need something like more feedback or want more career opportunities you ask for it. You try to find as many resources as you can that will help you and the place you work for.
When I first heard this term I thought it was someone trying to pass the ball. Then I later came to understand it was taking responsibility in the work place. Looking for resources, advancing your knowledge.