Social Darwinism

Social Darwinism is a term used for different movements. Charles Darwin was the main proposer of evolution. Evolution is a concept from biology that explains how different life-forms change over time. Most offspring are not exactly like their parents. Some of the children will have different features (or traits). These features may mean that some children are better adapted to the place where they live. If so, the children will have a better chance to survive and reproduce.
Social Darwinism theories try to use these ideas from biology for human society. They talk about a "Struggle for survival" of human societies. During the era of Nazi ideologies, the idea of Survival of the fittest combined with racism. They claimed the Aryan race was better than all the other races and therefore needed more space to live. This space was to be provided in the east (where mostly Slavs lived). 
Today, this is seen as wrong. There was no evidence that Slavs were, as individuals, any better or worse than Germans.
Although Darwin's idea was revered in most of the western societies, some Russian intellectuals did not accept his ideas. They feared that accepting Darwin's ideas would cause harm. One of Darwin's biggest critic was Leo Tolstoy, who felt strongly against what he thought was Darwin's idea. In a letter from his death bed, he warned his children not to take Darwin's struggle for existence as a moral guide. Darwin never suggested his ideas were a basis for human life, just a description of what had happened in evolution.
Social Darwinism takes the ideas from Darwin’s theory of evolution and uses it on society. Darwin believed that people who were more able to survive were able to have kids with similar abilities. Social Darwinism says that people who have more skills will become more successful. These people can spread their influence and change the politics and society around them to make it better for themselves. 
Proponents.
Herbert Spencer.
Herbert Spencer's ideas of evolutionary progressivism, stemmed from his reading of Thomas Malthus. His later theories were influenced by those of Darwin. However, Spencer's major work, "Progress: its law and cause" (1857), was released two years before the publication of Darwin's "On the Origin of Species", and Spencer's "First Principles" was printed in 1860.
In "The Social Organism" (1860), Spencer compares society to a living organism and argues that, just as biological organisms evolve through natural selection, society evolves and increases in complexity through analogous processes.
In many ways, Spencer's theory of cosmic evolution has much more in common with the works of Lamarck and Auguste Comte's positivism than with Darwin's.
Bad use.
Social Darwinism can be used as a drive for political parties. For example, the Nazis during World War 2. They preferred some people over others based on ideas like race, and the amount of political control they had. They did not like the Jewish people because they thought they were less than human and were not as important as the rest of the people of Germany. 
To justify war on the basis of race is common throughout history. It was very often used in the ancient world when nothing was known about heredity. Nothing that Darwin wrote ever came close to justifying warfare. Warfare has a much longer history than Darwinism. Its roots lie in the struggle for survival of groups of early humans, not in any modern science. Darwin, on the other hand, was basically a pacifist:
"... Social instincts lead an animal to take pleasure in the society of its fellows, to feel a certain amount of sympathy with them, and to perform various services for them".