A silver umbrella is used to reflect the light, of a studio strobe. The umbrella can be made of a black material on the outside. The way to use an umbrella like this is to fire the flash into the umbrella, and use the light that will reflect off the silver material, inside the umbrella. It is mounted, the same way as the white umbrella. But the strobe is to be turned away from the subject, so the reflecting light will be sent towards the subject.
Since the area of the umbrella is bigger than the light source - the strobe head, it will be softer.
A silver umbrella can be bought in a huge size (~180cm), which is recommended for use in portrait photography. Because of the size, the light being bounced from the umbrella will be softer, and can be used as the only light source, with you, the photographer, in front of it, - to have the light coming from behind the camera.