The simplest definition of natural selection is that it is the mechanism by which an organism that is best suited to its environment will survive and pass on its beneficial traits in increasing numbers to the following generations, whilst those organisms less suited to the environment will be eliminated.
For example, some cheetahs can run faster than other cheetahs and will therefore be more likely to catch their prey. Organisms that blend into their background and remain hidden from their predators will have a better chance of surviving than those members of their species that cannot. Basically if an organism develops a trait that helps it to survive, then it will pass on that trait to its offspring, eventually resulting in the widespread appearance of that trait in a population.
Now members of a species differ in a number of ways and the root cause of this variation is DNA; changes in genes and/or their regulatory elements can generate new beneficial traits. It explains design in nature. It is blind and unconscious and happens because of random genetic mutations throwing up new phenotypes. Although most mutations are harmful, every now and again there are genetic faults that confer some advantage to an organism. We can see examples of this everywhere.