I'd like to learn the applications of the multiple exposure function on my camera (D700), but I can't even figure out what the difference would be between using it and just using a single exposure at a slow speed. Obviously, I have a lot to learn. Could someone please help?
what the difference would be between using it and just using a single exposure at a slow speed
The difference is that you can take several completely different exposures all in the same frame. There are lots of ways you can use it.
For example, you could take a shot of a landscape and then a shot of a person against a dark background. The effect you'd get would a semi-transparent person layered over the landscape.
Another, perhaps more likely example: You can take several exposures of a single person in different poses in different parts of the frame. This works best with a black background, so that nothing in the background bleeds through the images.
A more common variation on the same theme is to fire a strobe multiple times during a single long exposure to freeze motion at several points.
This kind of thing was much more common in the film days. With digital, it's so easy to combine images in different ways after the fact that it's not necessary to do it in camera. It's still fun, though, and might get your creative juices flowing.
With a single long exposure everything that happens from start to finish is included in the frame.
With multiple exposures you can pause to allow changes to the scene to be made without the time during which those changes are made being included in the photo. You can even totally change the composition by changing aperture, focal length, or even to a different lens, where the camera is pointed, where the camera is placed, etc. This also frees you to use short shutter times. Two shutter actuations shot at 1/500 second each can be combined without the requirement that everything in both exposures happen within 1/250 second (1/500 + 1/500 = 1/250). Instead, you can take as long as you want between the two shutter actuations to recompose the framing or modify the scene.