Also called a tapered and flared, or trumpet barrel, it is a barrel whose breech and muzzle profiles are larger than it's center ( called the waist ) profile. The modern version of the swamped barrel is usually exaturated as compared to original barrels...
I'm just guessing, but I think the term Swamped is based on the higher breech and muzzle being similar to the two banks on either side of a swamp or lowland.