The brown spots on the whites of the eye usually caused by melatonin. They are the same as the causes of freckles and moles on the skin. In fact, they are usually harmless. You can completely ignore it. And so far i didn't heard any treatment that can remove them from the eyes naturally. If you really hate them, you can consult an eye doctor.
There are several causes of brown stains on the whites of the eyes. If they are pigmented spots a, it is normal and you needn't remove them. And in common, Asians and very heavily pigmented Caucasians usually have this problems. Also, some cosmetic surgery may cause scar formation thus make it look like a brown stains. If so, you can consult your eye doctor.