The "Ban Button" can refer to a number of things, whether it be a button on a forum or game that bans, or a key that bans.
The origins are not entirely sure of.
Admin: *Presses the "Ban Button".*
Person 1: Aww! I'm so angry now I'm going to threaten to take down this site with my bare hands yet I will not do anything because deep down inside I'm scared!