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A softbox provides a space for the light from the flash or strobe to bounce around before it heads out through a single or double layer of diffusion panel on the front. It is a great way to make the apparent size of your Speedlite seem much bigger. The advantage of a larger light source is that the shadows soften when the light comes from multiple angles—the same way that clouds soften sunlight.
This is my favorite of the Speedlite-mounted softboxes. It has inner and outer diffusion panels so that the light softens nicely. The 9″ square face is the largest among the group. The face is recessed so that there is a definite edge to the light—very helpful for feathering the light. It mounts quickly and securely to the Speedlite without any additional straps. It folds up quickly.