ND filters derive their name from the neutral effect they have on color while still darkening the image: absolutely gray, dimming all colors equally. This may seem simple, but it's a powerful tool. You've probably run across scenes that are just too bright to photograph the way you want to. This is where ND filters come in handy.
There are a three main varieties of ND filters: solid ND filters, ND filter wheels, and graduated ND filters. Solid ND filters are the most common out of the three, consisting of a single filter of even darkness. ND filter wheels are made with two glass disks that each have a gradient of increasing darkness which can be rotated relative to each other, allowing a whole range of light and dark to be easily manipulated by the photographer. Graduated ND filters are basically ND filters with a single gradient from darker to lighter. Use of these are covered in a different article.
ND filters tend to be classified by the “f-stop reduction”, that is, measuring how much darker the image is made by how much darker it would have otherwise been made by increasing the f-stop by that much. Another system of classification is by the percent of the light that passes through the filter, or transmittance.
Not all ND filters are created equal. Even the best of them will have a slight color cast. Make sure that you check out the quality of the ND filter carefully before purchase.
Don't have an ND filter? Check out this article for how to make a DIY ND filter.