Visceral literally means "pertaining to the interior of the body", and in addition to this literal meaning has two derived meanings.
First, visceral is often used as a synonym for gory. Hardly inapproriate, since most gory things do involve things that should, rightfully, be on the inside of the body. By extension, however, visceral can mean anything intense and perhaps violence, even if no actual cuts are made.
Visceral also refers to the sensations that reach us from the inside of our body, from the crude": "damn, I just drank three tablespoons of Tabasco sauce" to the sublime: "This view of the Grand Canyon is breathtaking". Although visceral is often used in American society to refer to emotional experiences that are somewhat unpleasent or overly intense, my own experience is that even very abstract, intellectual experiences have visceral feelings attached.