Some softboxes come with two layers of diffusion panels, a smaller one on the inside of the softbox very near to the light bulb and a large one that you place on the outer panel to cover the front.
|inner diffusion panel in softbox|
Not all softboxes have two diffusion panels, it is generally found on larger ones. The function of the inner diffusion panel is to spread the light evenly across the front diffusion panel. Without the primary diffusion panel light distribution will not be even across the front, there might be hotspots in the center and less light towards the corners.
Making light pass through an additional layer of diffusion material does two things, it softens the light a bit and also lose a little bit of light. The design of the softbox as well as the light you are putting inside has a very strong bearing on how even the light distribution is across the surface. Generally the larger the lightbox, the more you need to disperse the light evenly from the main source.
Having an extra layer of diffusion material does not mean you have to use them on all occassions, for example if you are using continuous light sources like the Westcott Spiderlites then it will be a good idea to take off the inner diffusion panel, as the light from those fluorescent bulbs are already soft and it is highly unlikely that you will get a hotspot in the center. Removing the inner diffuser makes it possible to get the maximum output out of the CFL’s. But when shooting with strobes it is better to leave it in place to get soft even light across the surface of your softbox.