Social darwinists were (mostly) a group of sociologists who tried to apply Darwinism to social issues, and mostly to answer the question of how the idea of evolution could explain the social world around them.
One of the most prominent social darwinists, Herbert Spencer (coiner of the term "survival of the fittest"), observed how people from colonized nations have worse situation in the world and attributed it to Darwinism - it must be that wealthy people are wealthy because they are better adapted to their environment - they are more evolved than people who are poor.
From there, his thinking went in the lines of "if the government helps the poor, it's interfering with the survival of the fittest, and worsening the state of the human species". The idea was poorly transfered from biology to sociology, probably to justify people's inactions at the time by saying that "it's ok because it's natural".
This has followed into the idea that letting the "inferior" part of the population die out would make the human race "more evolved", completely ignoring the that reducing variation hinders the effects of Natural Selection.
Endangered species are often found to have little gene variations in their gene pools - the less variation you have between species the closer you are to "inbreeding effect" leading to unhealthy population - high-variation population is generally a more healthy population, making eugenics totally nonsensical from biological standpoint.
Even though Social Darwinism carries Darwin's name, its logic relies on Lamarckian evolutionary model, which says that traits acquired through life can be inherited by the offsprings.
In summary, Social Darwinism is taking a good idea from biology and turning it into a bad idea in sociology by ascribing cultural differences to biological superiority.