It increases the damage of the weapon on which it is attached by 40%. This proficiency, although late to unlock, is highly recommended for all shotguns and is practically a necessity for the slower firing shotguns. For balance reasons, it is only available for use with shotguns.
Up until a hotfix, players were able to use Damage on any weapon via a glitch. This gave weapons like the M60E4 and MK14 a one shot kill ability to the stomach and up. Fourzerotwo, the former creative strategist for Infinity Ward, tweeted out that a patch would be released to prevent players from exploiting this glitch, weeks before the patch was made public. He also stated that 'glitchers' would receive bans. Whether these bans are permanent or temporary was not specified.
In effect, this proficiency is virtually identical to Stopping Power from previous Call of Duty titles, except only for shotguns.