"Visceral" means "coming from emotion rather than from reason." A "gut feeling," for example, can be described as a "visceral feeling." The word comes from the Latin root "viscera," which literally means "internal organs."
In medicine, "visceral" means "relating to the internal organs," a usage that remains close to the word's Latin roots. Although the literal, medical meaning was most prominent from the late 18th century, the figurative meaning slowly grew in usage after the 1940s when art critics used the word to describe their aesthetic reactions to artworks.
The root "viscera" is also in the word "eviscerate," which literally means "to pull internal organs out of." Colloquially, people use this word to mean "defeat badly," but in medicine, again, the meaning is very close to its Latin foundation.