A duster is a light, loose-fitting long coat.
The original dusters were full-length, light-colored canvas or linen coats worn by horsemen to protect their clothing from trail dust. These dusters were typically slit up the back to hip level for ease of wear on horseback and were the recommended "uniform" for Texas Rangers. Dusters intended for riding may have features such as a buttonable rear slit and leg straps to hold the flaps in place. For better protection against rain, dusters were made from oilcloth and later from waxed cotton.
In the late 19th and early 20th centuries, both men and women wore dusters to protect their clothes when riding in open motorcars on the dirt roads of the day.
Duster (clothing) Wikipedia
Western horsemen's dusters gained renewed popularity in the late 20th century and are now a standard item of western wear. They figured little in Western films until Sergio Leone re-introduced them in his movies The Good, the Bad, and the Ugly and Once Upon a Time in the West. The latter played for many months in Paris and was in part credited with a revival of the duster in men's fashions in that city. In modern times, leather dusters are worn by motorcyclists to prevent road rash.
Similarly, in the genre of heroic bloodshed, primarily through Chow Yun Fat and John Woo, the hero is often seen wearing a duster.