You set the shutter speed to be about a second long and then fire the flash when you take the shot. The flash is bright enough that everything in range will be able to burn out the things farther away as well as avoid camera shake, but the shutter stays open long enough that the thing in the background are bright enough too. They tend to suffer from camera shake, but if you move the camera on purpose, it looks cool.
In this photo, Tracie used the lens zoom to make the lights look like they were moving from the centre to the edge of the photo. In some of the other ones, we rotated the camera while the shutter was still open to make it look like the lights were swirling.
It's pretty easy to duplicate if you can force your flash and set the shutter speed at the same time.