A duster is a tool for removing dust. Sometimes it has an extensible pole to allow the user to reach a distant point, such as a corner where the walls and ceiling meet, so the user can remove spider webs.
Dusters were traditionally made of feathers or rags. Now, high tech fibers and cloths are used in many dusters.
For some people with allergies to dust, it may be helpful to wear a mask, like a surgeon's mask, over their mouth and nose when dusting. They may also want to vacuum it up instead of traditional dusting methods.