This sentence comes from Clint Eastwood's "Dirty Harry" movies, most particularly the the movie "Sudden Impact", where the lead character says the line to a criminal he wants to shoot. It means that Harry was just anxious for the criminal to attempt to shoot a hostage he was holding, since it would give Harry the opportunity to shoot him, which would "make his day."
An ex -American president, Ronald Reagan went on to immortalize the line in a speech about raising taxes.
Generally, "make my day" is an Americanism meaning to have something happen to you that makes you happy.