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The Roughness input controls how rough or smooth a Material's surface is. Rough Materials scatter reflected light in more directions than smooth Materials, which controls how blurry or sharp a reflection is (or how broad or tight a specular highlight is). A Roughness of 0 (smooth) results in a mirror reflection and roughness of 1 (rough) results in a diffuse (or matte) surface.
Roughness is a property that will frequently be mapped on your objects in order to add the most physical variation to the surface.