The Long Barrel increases the range of a weapon by 16%. Therefore, the longer the initial range of a gun is, the longer the maximum range will be. The attachment is available for submachine guns, shotguns and handguns. It is incompatible with the supressor attachment, for balancing reasons.
Call of Duty: Black Ops: Declassified
"Increased effective weapon range."
— In-game description.
The long barrel returns as the Extended Barrel.
Trivia
Call of Duty: Black Ops II
The only weapons to actually change appearance cosmetically when outfitted with the Long Barrel are the Executioner and the Olympia.
The Long Barrel doesn't actually increase the damage inflicted. Despite the statistic increase, rather it increases the distance of the damage drop-off by increasing the range.