In Fallout: New Vegas, it is a unique piece of clothing providing a bonus of +1 Charisma and +5 Guns, but lacks any Damage Threshold.
The Duster outfit seems to consist of a black undershirt and a pair of gray canvas pants underneath a long, brown leather overcoat with the sleeves rolled up above the elbow, a pair of leather gloves on the character's hands, and a pair of motorcycle boots for footwear.
One is given at 100% condition by Sonora Cruz if you join her group, the Regulators. To join the Regulators, you must have the Lawbringer perk which is available starting at level 14. Taking the perk will add the location of Regulator HQ to your Pip-Boy world map.
If you have negative Karma, Regulators will occasionally show up to kill you for a bounty, at which point you can obtain a regulator duster by killing them and looting their corpses.
If you have the Lawbringer perk and you reverse-pickpocket the un-named Regulators inside the Regulator HQ they will have a new duster in 72 hours.