In the short story "Compliments of the Season" by O. Henry, the main character, Fuzzy, is a tramp who restores the rag doll Betsy to its rightful owner: a spoiled rich girl. Fuzzy has had too much to drink on Christmas Eve and spies Betsy's leg partially buried, sticking out of the ground. Fuzzy retrieves the doll and takes it to Grogan's saloon. At the saloon are three thugs: "Pigeon" McCarthy, Black Riley, and "One-ear" Mike. They see the doll and also discover there is a one hundred dollar reward to return the lost doll to its millionaire owner.

Quickly, the three hoodlums devise the plan to get the doll from Fuzzy no matter what it takes. All three have weapons: a gas-pipe, a slung shot, and brass knucks. The plan changes as they follow Fuzzy to the millionaire's house. They decide to let Fuzzy get the reward, and they will attack him after he gets the money. These are career criminals. The brass knucks are described by O. Henry as an heirloom because an heirloom is a valuable item that is passed down from one generation to the next. In this way, the brass knucks, a street weapon, clearly show that "One-ear" Mike's family have all been thugs. Ironically, the thugs' plan backfires when Fuzzy is offered a ride in the millionaire's Mercedes.

In putting these two things together, the author is trying to tell us in a humorous way that One-ear Mike is a criminal and that he has come from a family of criminals.

Brass knuckles are, of course, used mainly by criminals.  There is not much of a legal use for something like that.  When the author says that they are an heirloom, he is implying that Mike's set of brass knuckles has been handed down to him from his ancestors.  This implies that Mike's ancestors were criminals just like he is.