Alright, hopefully you've found Episode 11 on ND filters interesting. These filters can certainly be quite useful and can be easily overlooked, especially by novice photographers.
The first half of the video was quite self-explanatory, so I want to jump right to the part about using ND filters to slow down your shutter speed or in other words allowing you to take longer exposures. Indeed, getting that silky look for streams of water during the daytime with lots of light would be quite tricky without such filters, but the same goes for shots of lightning.
Now before I get into this, I want to say that shooting lightning can and is dangerous. Simply said, I don't recommend doing it unless you have truly done your research about lightning safety and you know what you're doing.
A common way to get shots of lightning is by setting up your camera to take a very long exposure, say anywhere from 5 to 30 seconds pointing in a direction where you expect lightning to discharge. During electrical storms at night, this tactic works quite well, but during the day, you would likely terribly over-expose your photo; frankly at those exposure times your photo would probably be completely white.
But by using a very dark ND filter, like an ND8, and a small aperture, let's say f11 (or depending on your lens even smaller), you can reduce the amount of light entering your lens drastically, thus allowing you to shoot some stunning lightning shots during times when there's still a fair amount of sunlight forcing its way through the clouds.
And do check out the third link in the web resources section below. There's a fantastic article by Peter Bargh about ND filters, and the part I want to highlight is in regard to shooting a scene where people might be getting in the way of your subject. The example in the article is about photographing architecture with tourists mingling around, and by using an ND filter you can apply exposures long enough to make those individuals almost completely vanish off the image. Here's how this works in case you're not quite clear on it. Since people are generally in motion, wandering around the place, they don't stand in one place long enough to properly expose on the camera's sensor. But the scenery around you, the buildings, artwork, what-have-you, are stationary, thus light from those objects keeps steadily coming to more or less expose well on your sensor.
Jumping to the third use of ND filters in my video, there's actually not a whole lot more to say other than that if you are shooting with older camera equipment with particular limitations in shutter speed and aperture settings (perhaps sensitivity would come into play as well), then an ND filter could help reduce the amount of light to a point where the camera could handle the exposure. But really, I don't see this as a major issue these days; it was probably more common with older film cameras that had a max shutter speed of 1/1,000 of a second, and where you were stuck with a specific speed of film until you finished that roll.
As usual, remember to subscribe and check me out on Facebook where you can also become a Fan, and so you can stay up-to-date with my videos. Also, feel free to send me questions you have about photography, which I may answer on a future episode. Cya next time!