Overproduction is when there are more polar bears being produced than can survive.
Variation is when there is genetic variation within the polar bears; some of them have thin coats of fur, and others have thick coats of fur. Thin coats (white polar bears) are being selected against, and thick coats (tan polar bears) are being selected for.
The environment decides which polar bears live and which don't. For example, the polar bears' environment is very cold, so if a polar bear has a thin coat of fur, it is less likely to be able to survive and reproduce.
Polar bears compete for food, which decides if they survive or not. However, polar bears also struggle with their environment; some polar bears don't have thick enough coats of fur to survive and reproduce.
One of the variations is selected for and one of the variations is selected against. In this case, polar bears with thick coats of fur are being selected for because they can survive and reproduce in the cold weather, while polar bears with thin coats cannot.
Evolution and natural selection will take time to pick the most fit to survive and reproduce, and then all the polar bears will be the fittest for the environment that they can be. This means over time, there will only be polar bears that have a thick coat of fur because they are the only variation that survived long enough to reproduce.