It works the same way that homeopathic medicine, therapeutic touch, reiki, healing crystals, feng shui, dowsing, magnetic bracelets, talking with the dead, and about a zillion other psuedo-scientific devices and practices: by preying on a combination of need, hope, and credulity.
I think that is exatly what it is, a 12v DC LED light.
"we cracked open the FD-47 to find a simple circuit board for the LED lights."