What exactly does it mean to metabolize anesthetics too quickly?

Not concerning: I'm not sure what was intended when you were told that. If it was local anesthetic that wore off too quickly, it was probably not "metabolism" but other factors that affected the duration of numbness. If it was related to narcotic medication, there are differences in metabolism and duration of effect. If referring to general anesthesia, it may mean that you required more medication than "normal".

Quick anesth: It could mean that higher doses were needed to keep you asleep or sedated. It could also mean that someone had a hard time preventing pain with local anesthesia injection. Some studies have found red headed individuals to have higher anesthesia requirements.