|Inserting ND Filter into matte box|
There are at least two reasons for a matte box; to control stray light from entering the lens and fogging up the image and to facilitate the use of filters. Most important for me are the ND filters.
Neutral Density filters are the equivalent of sunglasses for your lenses, they decrease the amount of light entering the lens without changing the color or quality of light.
|Effect also known as "selective focus"|
The bottle in the foreground is barely in focus and everything else is a soft blur. Only fast lenses can accomplish this degree of blur at such a short distance. The lens, in this case, is wide open.
Imagine you are outside on a very bright day and you want to create this effect; to blur the background behind your subject. The problem is that you want to keep your shutter speed at 1/60 for 30fps video, which means that you would have to close the iris to get the proper exposure, remember it's very bright outside.
By closing the iris you increase the depth of field and more area behind your subject will be in focus. This is not what you want. You want to open the iris as much as possible to narrow the focus area. Here's where the ND filters come in. Like putting on sunglasses. With the ND filter installed you will have to open the iris to expose properly, therefore achieving selective focus or narrow depth of field.
Below is another example where the woman's ears are already starting to soften to a nice blur. For more on this subject see my other post on Depth of Field.