Social Darwinism is the general view of selection within societies being good for the species or that one's plight in life has to do with one's fiber, blood, character, superior breeding, genetics, race, class, etc. That the drunk who dies in the ditch earned his place in the ditch because he was somehow inferior to the businessman who inherited his father's fortune. That if we help the weak, heal the sick and educate the ignorant we are serving to weaken humanity because the weak are weak because they are inferior, the ill are ill because they are weak-blooded, the idiot is stupid because he is unteachable.
Social Darwinism suggests that somehow social situation is the principle result of ones abilities. That some people do well in business not because they had the opportunities and education and luck to succeed but because they are somehow more worthy and able in some intrinsic capacity. Social Darwinism is a hollow echo of actual evolution by natural selection.
In nature the geometric rise of populations of all organisms is checked by nature, predation, death, mate selection, starvation, illness, weather, and sometimes some of these attributes are a little better suited to a situation or a little worse and these improvements find they increase in the gene pool at a greater rate and keep doing so. So by sickness, death, and predation all organisms are naturally given to a propensity towards complexity, utility, adaption, and improvement spiraling off into the infinity of the unknown.
Now, we should notice stark differences between the two things. One is based on some nebulous idea of inferiority and the other is based on certain individuals doing slightly better as far as their genes were concerned. One has a vague idea that somehow peoples lots in life are their own fault or their lot, while the other recognizes the general struggle for existence. One asks that we withhold our mercy and condemn the victims of fate while the other asks that we do jack squat because it simply sits there explaining all the design of life. Social Darwinism is after all an argument about how we should act and general vague notions that that is how things should be or that they are somehow better that way. Whereas evolution by natural selection explains life whether we care or not.
While sometimes Social Darwinism finds political cover and adherents especially among the wealthy and affluent and gets rehashed over and over again in more modern social philosophies like Ayn Rand's Objectivism and finds strong comradeship with bizarre ideas about the need for anarchy as a system of government and deregulation to unbind the invisible hand of the market. That the world is better as a dog eat dog world because it demands we pick ourselves up by our bootstraps and become the captains of our souls and masters of our fate. Interestingly these related ideas find themselves properly opposed by the same thing that opposed Social Darwinism in the first place, actual evolution by natural selection.
Evolution, beyond simply being just a theory to explain the design of life, also finds itself properly applied in very diverse disciplines such as game theory, morality, and economics. It turns out the world isn't really best off as a dog eat dog world. In fact, one would be well advised to understand that the world isn't dog eat dog but that dogs are themselves pack animals and work together in cooperative groups. The invisible hand of the market isn't a magical wand but rather the economic equivalent of the blind watchmaker in biological evolution. And we should closely observe that the blind watchmaker doesn't craft simply efficient producers but is riddled with parasites from top to bottom. And that we should properly understand that cooperation is the natural propensity of evolution rather than necessarily competition. Markets will naturally gravitate towards parasitism or monopoly rather than simply producing the best product for the cheapest price. We should not nor cannot embrace the idea of letting the chips fall where they may while the greatest indicator for where you will end up in life is where you started in life.
Truth comes from understanding that we live in a cooperative society rather than a meritocracy and that the poor are not necessarily poor because of some vague sense of inferiority but rather more correctly because there but for the grace of God go I. That I was born in America has much more to do with my successes than my genes could ever account for. The fact that I was born to a middle class family and was able to go to college without trouble or incident, that I lived in a good neighborhood, that my country has public schools, that I went to honors classes, that both my parents are college graduates in the sciences. Dumb luck has more to do with individual success than anything else. Science has more to do with societal success than anything else. Morality has more to do with humanity's success than anything else.
Suffice it to say that Social Darwinism in all its iterations both old and modern are predicated on rather staggering errors, and evolution as properly understood within society, biology, and economics strongly indicates that our greatest prosperity will be seen not within the idea of laissez faire (hand's off economics) but in the domestication of our markets and the socialization of the essentials of modern life, the promotion of science and embracing of international cooperation.