Most new cars have polycarbonate (plastic) headlights which are stronger and lighter than the old glass ones. One key problem is that they tend to get scratched and discoloured over time. This makes the headlights appear dull and cuts the amount of light emitted to make your night driving safer.
What causes the oxidation?
The oxidation is generally a reaction by the plastic to ultraviolet light, build up of road grime, chemicals in the air (and rain) and can even be made worse by the water that you wash the car with. The ultraviolet light from the sun reacts with the plastic and grime to make the lenses cloudy. The heat generated by the lights can bake on the grimy film.
What can you do to remove it?
At some point this oxidation needs to be removed and there are many ways to do it; front using toothpaste (and a lot of elbow grease), common household chemicals through to professional kits. If the oxidation was on your reading glasses then you would have them cleaned straight away.
Preparing the surface and protecting the surrounding areas is vitally important otherwise cleaning the headlights may damage the paintwork and result in more work. You can purchase cleaning kits and watch how to Youtube videos but if you're not that handy, doing it yourself may not get you the shiny and clear headlights.
Sometimes the film may be hiding further damage like pitting and tiny cracks (crazing). Cleaning won't remedy this and you may need new lenses. This can be an expensive fix.
Have a good look at your headlights and if they appear obscured or hazy, call your local A Grade Automotive Network workshop and get them professionally cleaned.