The axioms of evolutionary theory can be simply stated, and understood by anyone. We divide them, roughly, into axioms of optimization and speciation. The former describes the "survival of the fittest" -- for some definition of "fit" -- while the latter deal with the division of populations into genetically distinct species. The variety of theories in modern evolutionary biology, and the bulk of professional interest, are directed toward the mechanisms of speciation; but it is the process of optimization which defines evolution for nonprofessionals.
So much is read into that one phrase, "survival of the fittest". When we begin to delve into its meaning, it seems that it is mostly tautological, and means essentially "survival of the most survivable". That is what an organism must be fit for. Another interesting part of modern biology is unravelling this tautology by finding the evolutionary use of mysterious characteristics.
In common parlance, this phrase is also given an economic as well as a biological reading, due to its common application to the competition among corporations. In this case, it is often assumed that there is no tautology because we can determine independently what "fittest" means [e.g., producing the best product, or having the lowest operating cost]. The assumptions underlying this reasoning are not always true -- consider Chrysler or more recently Fiat -- but they are not utterly invalid, and the "theory" of corporate evolution has some explanatory power.
Something else comes from this economic usage: the idea that evolution, or the competition it implies, is somehow a moral good. The positive principle, that the fittest are likeliest to pass on their characteristics to future generations, becomes conflated with the normative statement that the fittest should be those who survive.
This repulsive pseudo-morality immediately collapses when seen directly. In fact, it is the negation of all morality by the claim that whatever wrongs are done -- a strong man stealing food from a starving child in a refugee camp, an unarmed populace herded into ghettos for later extermination, a politically inept functionary sent to the gulags, a lone man standing in front of a row of tanks at Tien An Men -- are simply facets of a struggle for survival, instructive information about how the world works. Survival of the fittest, and all that.
It is not hard to recognize the illogic, as well as the immorality, of substituting Darwinism for traditional ideas of morality. But there is another problem just behind this, exemplified by the fact that you knew what I meant by "Darwinism" in the preceding sentence. The anti-evolution movement damages our schools, our children and our nation; and the conflation of evolution with Darwinism abets its spread outside the isolated camps of extreme fundamentalism. It is as if Adam Smith had been named Fasc.
We reject the idea that the strong is intrinsically good, but there is a moral lesson to be drawn from the theory of competition for survival:
What is good should be made strong.
[Update 12 July: corrected "inflation" to "evolution" in penultimate paragraph. Further thoughts here.]