Barrel Mods generally affect Weapon Damage in some way.

Explosive Optimization Barrel
Attachable to Rocket Launchers and Detonators. Mod Effect: Full Damage Radius.
Explosive Power Barrel
Attachable to Rocket Launchers and Detonators. Mod Effect: Damage.
High-Caliber Power Barrel
Attachable to Bolt-Action Sniper Rifles, Semi-Auto Sniper Rifles, and Pistols. Mod Effect: Damage.
High-Caliber Precision Barrel
Attachable to Bolt-Action Sniper Rifles, Semi-Auto Sniper Rifles, and Pistols. Mod Effect: Critical Multiplier.
Mid-Caliber Power Barrel
Attachable to Assault Rifles, SMGs, and LMGs. Mod Effect: Damage.
Mid-Caliber Precision Barrel
Attachable to Assault Rifles, SMGs, and LMGs. Mod Effect: Critical Multiplier.
Shell Power Barrel
Attachable to Combat Shotguns, Pump Shotguns, and Sawed-Off Shotguns. Mod Effect: Damage.
Shell Precision Barrel
Attachable to Combat Shotguns, Pump Shotguns, and Sawed-Off Shotguns. Mod Effect: Critical Multiplier.