A Big Bang is a specific type of challenge usually involving long fanfictions and accompanying artwork. This type of challenge is a reprise of the old zine tradition of collaboration between artists and writers for internet fandoms.
Like most Big Bangs, the South Park Big Bang have a similar format: Writers sign up and begin writing stories. When the early drafts of the stories are available, each one is assigned one or more artists, or artists might claim stories from posted summaries. Artists create fanart to go along with the story.