Tell me about "Gaited" horses

I've never been around people who had them, so I'm not clear on exactly what it means. My understanding is that it's like a 4th gait that certain breeds of horses have over and above walk, trot and lope/canter. I also understand that it's a really comfortable ride, but I don't know exactly what it looks/feels like. Is it also called "single footing" or is that something else?

I saw Cajun's video of Ben moving around inside the barn, but I couldn't really tell what he was doing. Can somebody link me to other vids of horses showing what it's all about?

Also, since I've been on this forum, I've heard a couple of abbreviations for horse breeds that I didn't know. What's NSH? I'm guessing something Saddle Horse?