Rice goes through a variety of processes before it's ready for cooking. After harvesting, the seeds are run through a rice huller/husker for milling to remove the outer grain husks. After this process, you're left with brown rice. Nice and simple.
To create white rice, there's added steps. The germ and the inner husk (bran) is removed, the grain is then polished, usually using glucose or talc.
The crazy thing is that these added steps to turn brown rice to white remove nutrients that are sometimes then introduced back in via synthetic sources - this is called fortified white rice. The same type of thing happens in brown bread vs. white bread scenario.
The loss of nutrients is broad and substantial. Plain white rice has far less Vitamin E, Thiamin, Riboflavin, Niacin, Vitamin B6, Folacin, Potassium, Magnesium, Iron and over dozen other nutrients. Added to that, the dietary fiber contained in white rice is around a quarter of brown rice.