If you aren't familiar with the movement in the La Cle du Temps, let me explain it. It starts with a tourbillon based movement, where the tourbillon juts out of the bottom side of the watch. This is called a vertically mounted tourbillon. You can see it in the picture looking like some space age propeller. The watch dial, to tell the time, is on the upper right of the dial. The lower left of the dial is a power reserve indicator (looks like 5 days worth in the manually wound movement), and above it is the selector for speeding up for slowing down the time. This is where it gets interesting, and Hublot has clearly changed the format of the dial a bit from the previous watch. Using a crown on the left of the watch you can alter the time to run fast or run slow. A fun, but gimmicky way of "controlling time." The neat part is that the movement always retains knowledge of the correct time - so you can always switch it back to "normal" mode and the time isn't all screwed up.
When is a watch like this useful? Honestly, I am not sure it ever is above and beyond appreciating the complexity of it all. In a sense, it is a metaphor about controlling time. The name of the watch itself is the "key of time." If you can afford it, you can say that you hold the key to time - and what greater power is there than that?