Social Darwinism can be defined as the application of Darwin's theory of evolution by natural selection to human society. This ideology achieved a fair measure of popularity in Western Europe in the late-nineteenth and early-twentieth centuries.
In very basic terms, it argued that societies operated on the same basis as the natural world, as nature "red in tooth and claw". In nature, the weakest species went to the wall while the strongest survived. This was what the Victorian sociologist Herbert Spencer, himself a social Darwinist, called "the survival of the fittest". And Spencer, in keeping with his fellow social Darwinists, believed that what applied to nature should, by extension, also apply to human society. That being the case, the weakest members of society should not be helped; they should be allowed to go under while the strongest human specimens survived.
Social Darwinism at work is prevalent in Zola's L'Assommoir. The story takes place against a backdrop of unimaginable poverty in a working-class neighborhood of Paris. Here, the main characters Gervaise and Coppeau must somehow rise above the filth and squalor to survive. Otherwise they, like so many others in their predicament, will go under, unmourned by a greedy, materialistic society that couldn't care less about them.
For a time, it seems that they have what it takes. Herbert Spencer himself would certainly have looked kindly on the couple's initially successful efforts at running a business. Unfortunately, their happiness is not to last, and it isn't very long before Gervaise and Coppeau are in serious trouble. This is because Coppeau suffers a serious accident which renders him incapable of providing for his young family, and which leads him to idleness and drink.
A social Darwinist would look at such a situation and conclude that Coppeau was a weak specimen after all and should be allowed to go under. As he's no longer a productive member of society, he shouldn't expect to be helped by either private charity or government assistance.
Eventually, Gervaise ends up the same way, and she and her husband both die in extreme poverty. Whereas normal, decent human beings would express sorrow at such a tragic demise, social Darwinists would be pleased to see natural selection in society doing its thing.