This phrase seems to be a humorous reference to the popular concept of “Six Degrees of Kevin Bacon,” a game based on the “six degrees of separation” theory and using actor Kevin Bacon. It suggests that any two people on Earth are six or fewer acquaintance links apart. In scientific terms, if a “Degrees of Kevin Bacon” gene has been identified, it could mean that scientists discovered a gene that interacts heavily with other genes or has a significant amount of mutations that connect to a range of genetic conditions, behaving somewhat like Kevin Bacon connecting various movie stars through film roles.