This is a Lastolite All-in-One 40" Umbrella. It starts out as a translucent umbrella, which may be used as a makeshift softbox, for aiming a light through.
The white insert may be added to transform the umbrella into a bounce umbrella, to soften the light in use more efficiently.
The silver insert is also used to bounce the light, but it adds a specular, or harder quality to the light that falls on the subject.
Use this size umbrella for headshots, or 3/4-length portraits, or small product setups.