ND filters are basically (very basically) sunglasses for your lens

If you want a long exposure they block the light light and allow your lens / aperture to be "open" without the picture just being white from over exposure

Try setting your camera to "bulb" mode or a long (even a second or two) exposure time and take a pic - it will be just white

By blocking the light (or most of it, you can get grades of filters) you can get different effects or allow you to get pictures you cant without the filter

An example of this is when you see "soft" or "blurred" water or clouds like:



The "softness" of the water is by a long exposure (and thus getting the movement of the spray from the water) which you couldn't do without a filter

Here's a with / without:



The lest hand site is a "normal" shot the right is long exposure with an ND filter

I've heard of people using ND filters to block out light pollution during star trails a "graded" filter (one half a dark filter the other plain) to block out light from a horizon or something

Not something ive ever done, so was just curious

So, are you stitching a time-lapse set of images or a long exposure to get the trails ?