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ND filter

A ND filter absorbs all colors of the spectrum evenly. That's why it's called neutral. And it's called neutral density because the glass has a certain (grey) density as to hinder a certain amount of light to pass through. Why?
When you want to take picture in light conditions that are so intense that your aperture and your shutter speed cannot resolute the surplus of light, you need something to stop it before all that light reaches your camera. Just like a couple of sunglasses for your eyes.
Another purpose might be the creative need to use a wide open aperture (unscharp back ground) or a long exposure (object movement). The use of a ND filter will give you the leverage you need.

Factor

With Hoya the amount of reduction can be recognized in the filter name. A ND2 filter bisects the light passing through; you can double your exposure time or aperture. With a ND4 filter you can quadruple the exposure time or aperture. That's easy to grasp, right.
Nonetheless, there are other filter brands that rather use obscure logaritmic integers, like 0.3 of 0.9. Why that is we don't know, but we know by experience that most photographers favor the logical factors that Hoya offers in the name.