"To impress the manager" means to make a positive and lasting impression on the person in charge. It usually involves doing things that make them see your skills, abilities, and hard work in a favorable light. Full definition
The captain has fallen dramatically and needs to impress the manager in order to win his place back in the team. (mufclatest.com)
If you talk nonstop in an effort to impress the manager with all your expertise, he or she may assume you would also talk nonstop if you were hired. (inc.com)
With such an important season, everyone will have enough chances to impress the manager if we are to compete on four fronts. (justarsenal.com)