The principles of evolution dictate that those with beneficial mutations are more likely to survive while those with non-beneficial mutations will fail. Likewise there are sometimes non-beneficial traits that people possess that make them more likely to "fail." These things can be genetic or developed elsewhere. Things like health issues, chronic conditions, disabilities, etc. The idea of Social Darwinism in it's most extreme is that it is natural that these people fail, and that society shouldn't feel responsible for taking care of them. Basically, it's a dog eat dog world.
How it works
While some people might have arguments about whether or not we can save money on health care by giving the government more control in regulating costs vs offering incentives for organizations that self regulate Social Darwinist's know the best way to save money on health care is to not pay for it in the first place! It turns out you can save tons of money by adopting Social Darwinism. Balancing the government's budget will never be easier... in fact why have a governmental budget at all? People should take care of themselves, right?