Well, as far as improving the image... that's quite subjective. A ND filter will allow a significant decrease in the light which is allowed to enter the lens and thus reach the film plane. They are sold in a few different 'powers', from the normal one, two and, three stop filters, to the darker ones like eight or ten stops. So, a ten stop filter would decrease the amount of light by ten stops, thus allowing for some fairly long exposures even in bright sun.
The typical use for ND filters is to keep very bright parts of the image (sand or snow) from blowing out. They are also sold in graduated filters which would allow for a scene such as a sunset or sunrise, where the sky is brighter than the foreground to be more evenly exposed.
That's a pretty basic definition... Hope that helps.
-Jason