Darwinism is the idea that species of animals evolved through natural selection. This means that the kinds of animals that were best suited to a given environment thrived and passed on their genes and eventually could create new species. This idea gave came to be summarized in the phrase "survival of the fittest."
Social Darwinism took this idea and applied it to human societies and to groups and individuals within those societies. It argued that the people who prospered (who became rich and powerful) must be the "fittest" in that particular society. This implied that they deserved to be rich and powerful and that other people deserved to be poor and weak.
This idea also implied that governments should allow ruthless competition between people. Governments should let people compete with one another so that the "fittest" people could rise to the top of the heap.
Social Darwinists, then, believed that human societies were like natural ecosystems. In both, the organisms that are the most fit will survive and prosper. They belived that society should be set up to allow for lots of competition so that people could become rich or poor depending on how "fit" they were.