Fog lights provide a low-mounted light source to illuminate the road surface in front of your car. They're an additional pair of headlights -- think low, low-beams. By illuminating the road surface in a low, wide fan in front of your car, the light doesn't shine directly at the precipitation -- rain, mist droplets or snowflakes -- in front of your car and reflect back into your eyes.
The idea that yellow lights would help you see through fog is a myth. The notion was that long-wavelength light -- such as yellow -- would reduce the amount of light scattering among the fog droplets in the air and allow you to see farther in foggy conditions. From a scientific standpoint, this argument doesn't hold up and you rarely see fog lights with yellow lenses anymore.
