Internet slang meaning that a person is being banned from access to something, usually an online multiplayer game such as World of Warcraft or City of Heroes.
John: What happened to Joey?
Jill: He got slapped with the ban stick for hacking.
Getting caught at school on a prohibited website. So your username on the network gets the ban stick. Basically, you're screwed for the rest of your school career with the ban stick.
Usually, others know you got the ban stick and will ridicule you for it.
Student: Yes! Bangbros
Teacher: What is this!? Go to the principal's office!
Classmate: You're gonna get shafted and the ban stick!