Take varieties of rabbits, gray, white and black, then put them in a snow covered environment. Which variety is going to predominate over many generations? That's easy, the white rabbit because they will blend in with the snow and not be seen by their predators as easily. The genes of the white rabbits will tend to be inherited by more and more offspring as they survive to the age of reproductively and mate with other white rabbits who also survive. This will continue until there are very few darker rabbits which is to say very little genetic material that creates the darker fur. This is know as adaptation. Really it is a form of mimicry. It is beneficial for the white rabbits to be able to "mimic" the white snow. The rabbits did not plan it this way, natural selection just favors them.
One wild example of mimicry is the Polyphemus Moth. This moth's coloring and patterns on its wings has an uncanny resemblance to an owl's head and face. Apparently the owl, who likes to eat moths will be fooled by the disguise and not eat the moth thinking it is actually another owl. Certainly this will benefit the moth, at least from the danger of being eaten by owls and other prey who might want to avoid tangling with an owl. Again, this moth knows nothing about it's ability to protect itself mimicking a moth; it benefits nevertheless.
The most famous example of adaptation given as a textbook example of evolution at work is the story of the Peppered Moth. There are light colored, dark colored and speckled varieties of these moths in the natural population. Evidently, these moths would hang out on the bark of trees most of which in their habitat had light colored bark. Consequently the lighter moths predominated in the same way as the white snow rabbits do. This was before the industrial revolution in England. When the factories produced enough soot over the years to turn the bark a dark color, it was noted that the darker moths began to predominate. And finally when environmentally conscious modern factories began to clean their act up, the dark bark became light again and logically the lighter moths are now predominate again. This story demonstrates the ability of a population of a certain species to genetically adapt and change their make up over many generations due to changing environmental conditions.
Does this adaptability of a species demonstrate evolution? It depends on you idea of evolution. If you mean the ability of a species to shift their gene pool over time to favor one trait over another, then yes. No problem with that. But if you mean the ability for a species to gradually become something completely different and higher in sophistication and complexity then absolutely not.
Notice that in the stories given, no moth changed it's own color, nor did any new rabbit become something other than a rabbit. Nor did any new colors turn up. The genetic variability built-in to the gene pool allowed for all the variability at the beginning of the story. No new information in the genes was produced. Instead, if anything, the gene pool tended to loose information. If all you had was white moths with no recessive genes for producing dark moths, then the dark moths would have become extinct. The fact that the pepper moths were able to shift their demographics from mostly white to mostly dark and finally mostly white again demonstrates the ability for the species to preserve themselves, not to become something other than what they were.
So adaptation is a nice feature of genetics. Is it perhaps a feature that has been designed to preserve the species during hard times? That would be what we would expect of an all-wise and gracious God.