Neutral density filters, usually called ND filters, are filters that actually interrupt all colors in the given frame because of their grey appearance. The over all purpose of the ND filter is to cut down on light in a situation without causing too much impact on color quality.
When light is reduced color tends to change. The ND filter counters that by creating a filter that changes all colors inherently, which preserves them as light is reduced. With the ND filter you can change things like aperture and depth of field and still cut down the light in the way that you want.
For example, if you want to open up the aperture in an effort to reduce the over all depth of field the ND filter will help you cut down on the increase of light. In the end the neutral density filter is just a method to cut down on light if it is too bright in your given situation.