If you ever thought that the concept of natural selection was easy then you must read Understanding Natural Selection: Essential Concepts and Common Misconceptions by T. Ryan Gregory. The article appears in the latest issue of Evolution: Education and Outreach and it contains many references to studies of how students perceive evolution.
Natural selection is a non-random difference in reproductive output among replicating entities, often due indirectly to differences in survival in a particular environment, leading to an increase in the proportion of beneficial, heritable characteristics within a population from one generation to the next......It is one of the core mechanisms of evolutionary change and is the main process responsible for the complexity and adaptive intricacy of the living world. According to philosopher Daniel Dennett (1995), this qualifies evolution by natural selection as “the single best idea anyone has ever had.” Natural selection results from the confluence of a small number of basic conditions of ecology and heredity
“There is probably no more original, more complex, and bolder concept in the history of ideas than Darwin's mechanistic explanation of adaptation.” Ernst Mayr (1982, p.481)
http://conservapedia.com/Natural_selection "...The fundamental statement of natural selection is that heritable traits which are beneficial will tend to become more numerous in successive generations, while heritable traits which are harmful will tend to become more scarce. The traits are defined to be beneficial if they become more numerous in successive generations. This principle is general, and applies to any system of individuals which reproduce; it is most commonly applied to systems of living organisms. It is sometimes summarized by the slogan, survival of the fittest...."
Reduce: "...The fundamental AXIOM of natural selection is that traits which are beneficial will become more common, traits which are harmful will become less common. This AXIOM is general, and applies to all of logic, unifying space and time in a sense; it applies to all of logic in all domains......"