Why are smooth items reflective?

All items are reflective. Rough surfaces reflect and scatter incoming light in all directions, that is why they appear dull. So if you look at a rough surface, the light that is coming from the object and into your eye, is a mix of light of various directions that hit the object before being reflected.
Smooth surfaces reflect light in one direction, based on the angle of the light it reflects, so the light from the object that hits your eyeball came from one source, which is why you can see a reflection.