Neutral Density Filters are designed for the purpose of reducing the amount of light entering your camera without changing the colour. The reason for the deliberate decrease of light is so that you can choose a slower shutter speed or a wider aperture maintaining a low ISO for maximum image quality. These Filters come in various densities depending on your needs for e.g. one stop (ND2), two stops (ND4) 3 stops (ND8) etc through to over 8 stops (ND400) and even the Big Stopper 10 stops.
The most common use for these ND filters is to achieve motion blur in landscape photography with waterfalls or waves looking silky and smooth. How much blur will depend on the density of the filter you choose, making sure for sharpness you have selected a high aperture. Combining a Circular Polarising Filter can also be used.
Another reason you might use a ND filter is for a shallow depth of field selecting a wide aperture when the light is too bright to achieve this. You may what a softer background in this light or a more appealing portrait using this technique.
You may want to try long exposures using ND filters to create empty street scenes which can look very dramatic, void of people and vehicles.
What you can buy.
The range of ND filters come in a round screw on or square drop in style requiring a holder which attaches to the front of your lens. The drop in type filters are available graduated meaning that only one side is darkened and you can place carefully in either the top or bottom so that your image can differs in exposure to the other. For example, a sky might be far too bright than the dark green landscape.