Jack's mask entices Bill, Sam and Eric to let go of civilization and to give in to their primal, animalistic natures. For Jack, the mask frees him to pursue his suppressed feelings of violence, anger and savagery without accountability or fear of shame or self-consciousness.
When Jack wears the mask, his behavior not only scares Bill, but it also draws Sam and Eric away from tending the fire. The fire is their only hope of being rescued, so by forsaking the fire in order to hunt with Jack, the boys are essentially casting aside their civilized identities. The transformation of the boys is complete once they follow the masked Jack and kill the pig together.