1. to (intentionally) not hear (It does NOT mean "to overhear" in the sense of hearing something you shouldn't. It is about NOT hearing something you normally should hear. Often used in context of ignoring remarks.)
2. to hear too much of something ("sich+Dat etwas+Acc überhören" - like eating your favorite food too often and you get to a point where you don't want it anymore. Not very common.)