In a social context, pushing the BigButton means to exercise one's authority to evict the membership of a community en masse. This kills all social processes, hence the analogy. This can be done in any community if one has sufficient power; it is most available to the GodKing of an online community, who can directly control membership via technical means. --XiongChangnian
Compare ShieldsUp, Big Red Switch (http://catb.org/~esr/jargon/html/B/Big-Red-Switch.html).