The future, as George Orwell would have it, is grey. We can supply it in varying strengths and configurations, we might add, and it in different diameters. Big Brother would approve.
The neutral density filter makes things go darker. You can make things go darker by one f stop - or two, three, four, six , nine, or ten stops quite readily with commercially available products. You can get filters that allow variable density from 1 to 8 stops - just by rotating the filter. You can get filters that start out at the top with a dark patch and then fade out half-way down. You can even get in-built neutral density filters in some special cameras.
The uses that people out these humble little bits of glass or plastic to are manifold:
Landscape shooters position the partial filters so that bright parts of their scene are brought into the camera at a lower intensity - the sensors then cope with the highlights much better.
Special effect photographers stack up extremely dark filters to allow long exposure times - and eliminate people from cityscapes or convert moving water to flowing mists.
Photographers who need to balance flash with daylight and high shutter speed sometimes need to use neutral density filters to make the complex equation work.
Videographers can use the variable density filters to provide fade-out and then fade-in scenes. The variable ones are a bit of a risk for some stills shooters as the angle that the filter may subtend might mean that odd patterns occur during shooting - video people rarely have this problem. Smaller sensor or the fact that the scene is there and gone?
The advent of the frame systems for filter holding ( Cokin, Lee, etc.) meant that rectangular filters could be made that slid readily up and down in front of the lens for the partial blocking of the scene - the graduated ND filter. These are readily available with either a sharp or a gradual transition between density and clear - you pick which makes the image look the best then slide the thing up and down until it matches.
Note: Popular legend has it that Cokin neutral density filters have a colour tinge that the other brand does not. I cannot see it myself, but it's not worth arguing about. Nearly all good DSLR and mirror-less cameras have fine tune adjustment of magenta/green in their menus and if you think you can see something you can crank in a bit of green. You could put it in as a custom channel, I shouldn't wonder.
I am pleased with the 3X ND filter in my Fujifilm X-100. It enables me to use a slower shutter speed out in the sunlight if I am using a higher ISO for the extra dynamic range it provides. And it is just a button click in the menu. The trick is to tie a string around your finger to remind yourself that it needs to be turned off later...