Long exposure photographs are highly popular in the landscape photography world, particularly when there's water in a shot. And while it's a great effect, sometimes, you don't want the long exposure to affect the entire image, which is where this neat technique comes into play.
Coming to you from Gary Gough, this great video shows him as he combines a long and normal exposure of the same scene for a very interesting final image. I found the effect particularly arresting, as my eyes expected reflections of the detailed sky on the water, and the lack thereof gave the photo a very peculiar and imaginative look. You'll need an ND filter to create the long exposure, but be extremely careful not to bump or disturb your setup when removing it between the long and short exposures. By keeping your tripod and camera in the same position and alignment between shots, you'll make aligning the different exposures and the overall post-processing go much more easily and quickly. And of course, you can experiment with varying levels of long exposure; as Gough mentions, leaving just a bit of motion in the sea can create a very nice effect and can also make the sky and water look a bit more harmonious. Try it out yourself!
To me, these tricks have always looked silly and gimmicky. They just don't make sense, logically, and it's a pretty weird "artistic concept" that doesn't really seem to have a point other than obvious eye-trickery just for the sake of being, well, eye-catching.
For the record, I do blend long and short exposures for portraits often, when clients want the certain look, and when it could seem plausible that a human subject could hold still for a certain amount of time. I also have done it before in nightscape photography, when representing a "static" night sky (pin-point stars) and a relatively long exposure for the earth, whether for sheer exposure reasons or for a light painting / trail reason. So, I'm not entirely opposed to the concept. I just think that the more unbelievable the images get, the more it seems like a gimmick.
/hypocritical soap box.