Bear and fish both struggle to survive. This bear, by catching the fish, is succeeding in the struggle and surviving. The fish did not survive, however, but left more fit fish behind.
This wild goat is well equipped with a lot of hair, which its ancestors evolved long ago and which helps it to survive cold mountain weather.
Darwin's Theory of Natural Selection has been divided into five parts to explain clearly how evolution happens in nature.
1. Organisms produce more offspring than actually survive.
Organisms can die from many causes: disease, starvation, and being eaten, among other things. The environment can't support every organism that is born. Many die before they are able to reproduce. One hundred (100) beetles can produce 6.1 x 1028(61 with 27 zeros after it) offspring in only 82 weeks (less than two years). Each beetle weighs 10 mg, and if they all survive, their total weight after 82 weeks would be 6.1 x 1021 (61 with 20 zeros after it) metric tons, equal to the weight of the entire earth. Obviously, their environment can't support all of these beetles, and many of them die.
The fish eggs at left are only a small fraction of those laid by a single fish. If all of the fish hatched and each of them laid as many eggs, which all hatched as well, there would be too many fish for the fishes' environment to support. 
2. Every organism must struggle to survive.
One reason that not all organisms survive is that there are not enough resources, things that they need, to go around. Organisms must struggle to get what they need to survive, competing against other organisms that want the same things they do. They also have to struggle to get away from predators and to overcome disease. For example, a fox struggling to catch a rabbit, which struggles to escape. As explained in part one, not all of them make it.
3. There is variation within a species.
Not all of the individuals in a species are exactly the same. There are variations, differences, among members of a species. If you look at the spots on several different ladybugs, or the stripes on zebras, you will notice that they don't all have the same number or arrangement of spots or of stripes. In addition to these easily visible variations, there are differences in skill and behavior, such as differences in how fast the zebras can run. If organisms were all the same, none would be better suited than any other, and selection could not occur.
4. Some variations allow members of a species to survive and reproduce better than others.
If an organism has a trait that helps it survive or reproduce, it is more likely to survive and be able to reproduce. A faster cheetah is more likely to catch a gazelle and survive, and a faster gazelle is more likely to escape the cheetah and survive. A showier flower is more likely to be noticed by a bee, which enables it to reproduce. A thornier cactus is more likely than other cactuses to be left alone by animals, rather than be eaten and die.
5. Organisms that survive and reproduce pass their traits to their offspring, and the helpful traits gradually appear in more and more of the population.
Most of an organism's traits are passed on to its offspring. If more of the organisms with the helpful trait survive, then in the following generations, more and more of the population have that trait. If there are some faster cheetahs and some slower cheetahs, the faster cheetahs will be better able to catch food and survive. With more of the slower ones dying before they can reproduce, and more of the faster ones surviving and reproducing, over generations the population on the whole will gradually become made up of faster cheetahs.
Here is an example demonstrating each of these points, told as the story of a population of brown hares in a polar region becoming white hares:
1. There are hares living in a cold, snowy, polar region. All of the hares are brown* and many of them are killed and eaten by other animals each year, so more are born than survive.
2. These hares are competing for life and struggling to survive, partly by trying to avoid predators, to "not be the one who gets eaten."
3. Each hare is a little bit different from other hares, but one time a few hares are born albino, white, because of a mutation in the genes.
4. This variation in color helps the albino hares to survive. Against the white snow, predators have a harder time seeing them, so more of the albino hares are able to survive and therefore to reproduce.
5. In the next generation there are more white hares, because the white hair gene is passed on. In this generation, too, more white hares survive and reproduce. They pass the albino trait on to their offspring, who also survive and reproduce more than do the brown hares. Gradually, there are more and more white hares in the population, until the entire population is made of white hares.
* You might ask: What were brown hares doing in a polar region? The brown color in an Arctic region was caused by one of two things, both of which are major causes of change and the arising of new species. One possibility was that a group of hares migrated from a warmer region and became isolated, the other is that the region where the hares lived became colder.