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 suppressor 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.
Call of Duty: Black Ops III
The Long Barrel appears as an attachment for several weapons in Call of Duty: Black Ops III. It only increases the minimum damage range of a weapon, meaning if a weapon takes a maximum of 5 shots to kill, it only increases the 4-shot-kill range. Aesthetically, it adds an extension to a weapon's muzzle. It is now compatible with the Suppressor barrel attachment.
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.