Natural selection is the process through which species that are best suited to their environment survive and reproduce at a higher rate than other members of the species. The most successful organisms are the ones with genes that allow them to out-compete their rivals. When reproducing, their fit genes will be passed on to the next generation. Eventually, every animal in the species will have the fit genes - meaning the species gradually evolve over time.
Differential Survival & Reproduction
A population of rabbits live in this area that experiences snowfall year-round. Their physical attributes - the different coloured fur - are determined by the encoded traits in their DNA. Some features may have been caused by a mutation that occurred when the DNA replicated itself during the reproduction, which could be a reason as to why there is variety amongst them. The traits that set them apart will allow these rabbits to go through the mechanism of natural selection.
Adaptation - Change in the Gene Pool
Some gene mutations can lead to favourable results, but in this scenario, the darker coloured rabbits will have a more difficult time surviving, due to selective pressures. This is because unlike the white rabbits, they lack the ability to camouflage with their environment, due to the variation, causing them to be easy prey for their predators, like foxes, coyotes, and wolves. Rabbits are also known to produce a plentiful amount of offspring, leading to the generations competing over limited resources.
Because of the variations, certain individuals of the population to survive and reproduce more effectively than the others. The selective pressures will lead to an evolution for the rabbits by acting as the driving force to indicate the most "fit" type of rabbit. Because of this, the unfavourable traits of having a darker fur-tone will be less likely to make it to the reproduction stage, meaning that this attribute will slowly die off with them, and leave the offspring with the beneficial heritable traits that helped the survivors.
The helpful variation will allow the "selected" rabbits - the ones who are best adapted to their environment - to be the majority of the rabbits that survive. Because of this, their reproduction will be at a higher rate, granting their offspring with the same heritable traits. The long-term effect of this is that eventually, white-furred rabbits will be the only type left, since they were best suited for the environment and were able to continue to pass down their heritable traits.
Ultimately, only the fittest will survive in their environment and be able to create more offspring. Natural selection is not random. It occurs in response to environmental pressures - temperature, geographical features, habitat - and results in adaptation, where organisms with certain traits have the best reproductive success. These traits are heritable, meaning that they are not acquired, but rather traits that are directly linked to the containments of your DNA.