A ban hammer is an avatar depicting a club, used to threaten banishment by antisocial bullies who become moderators at forums & virtual communities.
Its an offensive picture used to intimidate people, by nazi-like creeps at forums who become mods or admins because they have no creative abilities, friends or respect for others; so they lurk about bullying & abusing people as a way of feeling superior & powerful in the community (when clearly they are most inferior as evidenced by their lack of useful abilities to contribute with otherwise)
As in life, the antisocial, mean & dumb are the ones who go about abusing & threatening people to inflict rules...rules being useless constraints picked arbitrarily, not so much for the purpose of prohibiting an unwanted behavior, but more as an excuse to commit abusive acts to show "who's the boss of who"
A "ban hammer" picture is designed to imply these bullies are to be feared. Bullies only know how to feel okay by making people scared of them. It gives them a weird dirty thrill. This is why they get excited by a picture of a hammer being used to violently destroy other people's stuff. This is why they like & use the "ban hammer" avatar.
Mods, banning, & report buttons are the things that ruin otherwise perfectly good fun, friends & being creative, at forums and virtual communities
The ban hammer avatar symbolizes this kind of pointless interference and repression, which is valued only by bullies seeking excuses to exist.