When something's visceral, you feel it in your guts. A visceral feeling is intuitive — there might not be a rational explanation, but you feel that you know what's best, like your visceral reaction against egg salad.
Your hatred of mice may not be rational, but it is visceral, and every time you see one, you feel like you're going to faint. And when you had to decide whether you were going to stay in Florida or move to Texas, even though you had a good job in Orlando you had a visceral feeling that Texas would be the right choice . . . and it turned out you were meant to be a rancher! Visceral can also mean “relating to the viscera,” with viscera being your organs.