This is a Smith-Victor 32BW 32" Black/White Umbrella. Umbrellas soften, broaden, and slightly diminish the light output of any tungsten or flash light source.
Umbrellas with a white interior will soften and weaken light more than an umbrella with a silver lining. Silver umbrellas also soften light, but not as much as white umbrellas. They do not diminish the light as much as white umbrella.
White silk, and taffeta umbrellas without a black backing or with a removable black backing may be used in the traditional bounce method, or as a makeshift shoot-through softbox, although the use of the light will not be as efficient as with a closed-sided lightbox.
There are umbrellas that change the hue, or tone of the light. There are umbrellas that change tungsten lights to daylight balanced lights. There are umbrellas that bounce the light, then soften it even more on the way to the subject. At this point, we cross over into Softboxes, which is covered in Softboxes.
Choice of umbrella size is determined by the size of the subject, and the strength of the light supply being used. Choosing an umbrella surface is as subjective as choosing a brush and paint.