Social Darwinism is a term used for different movements. Charles Darwin was one of the main discoverers of evolution. Evolution is a concept from biology that tries to explain how different life-forms change over time. It basically says that because most children are not exactly like their parents, there is change. Some of the children will have features (or traits). These features will mean that some children are better adapted to the place where they live. They will therefore be better able to have offspring. Some of the offspring might also have the trait of their parents.
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. Since the Aryan race was better than all the other races, it needed more space to live. This space was to be provided in the east (where mostly Slavs lived). Today, this is seen as badly named. Most of the ideas for the theories are from Lamarckism and not from the theory of evolution, proposed by Charles Darwin.