Polar bears have white fur because it serves as camouflage in the Arctic snow, allowing them to blend into the environment and hunt. Polar bears, having evolved from grizzly bears thousands of years ago, also changed in other ways to survive in their habitat.
The fur of the polar bear, despite popular belief, isn't actually white. It is transparent and reflects visible light, which gives it a white appearance. The shade of white varies on the time of year. The fur takes on the most brilliant shade of white just after the bears shed in the summer. Algae growth in polar bears' fur can even turn the animals green, which is a common occurrence in zoos.
Polar bears have dense fur that keeps them from losing body heat in the Arctic. Scientists believe that the keratin on the hairs absorbs ultraviolet light to keep the bears warm. Although bears do have a layer of fat, their thick coat is their primary defense against the cold. The fur is so efficient that the bears can overheat when they run. The fat layer does benefit the bears while swimming in icy water because fur does very little to keep them warm when it is wet.