The Dawn Treader

Galton, heavily influenced by Darwin's work on natural selection, began to consider breeding as it applied to human beings. 

"Galton was struck with an interpretation of Darwin's work where the mechanisms of natural selection were potentially thwarted by human civilization, and since many human societies sought to protect the underprivileged and weak, those societies were at odds with the natural selection responsible for extinction of the weakest. Only by changing these social policies, Galton reasoned, could society be saved from a "reversion towards mediocrity"—a phrase he coined in statistics which he later changed to the now-common, "regression towards the mean."
Answers.com: Eugenics

Galton's idea was basically simple.  Improve our society through good breeding (positive eugenics) among humans, and by avoiding bad breeding (negative eugenics).   Galton's fear was that the inferior (i.e. hereditarily weaker) human beings would out reproduce the superior ones.  This would be a catastrophe in Darwinian terms.

Galton's ideas took hold in America.  None other than Alexander Graham Bell was an enthusiastic supporter of the concept of eugenics.  Eugenics became an academic discipline at colleges and universities.  The amazing history of the American Eugenics movement is captured at this excellent web site.  I commend it to you for further study.  The American eugenics movement fell out of favor in the 1930s.  That was not true in Germany, however.

Galton's ideas resonated with German intellectuals in the 20s.  Germany had lost many of its strongest and bravest in the great war.  The genetic stock was depleted.  Instead, the country was populated with those who were too weak or who sat out the war.   The cost of taking care of the mentally ill, furthermore, was burdensome on Germany's war torn economy.  Eugenics and "scientific racism" found traction.

They embarked on the most aggressive program of eugenics in history.  They practiced negative eugenics in the form of compulsory sterilization and euthanasia of those whose life was deemed unworthy of life.  This included not only the incurably ill but large segments of the mentally ill, the feeble minded, the retarded and the deformed -- children and adults alike.  They also practiced positive eugenics otherwise known as the "battle for the births".  Abortions were prohibited, but sterilization courts could rule that pregnancy could be interrupted for eugenic reasons in a “racial emergency” situation: that is, if the future child was likely to inherit certain defects or (in all probability) had mixed (Jewish and non-Jewish) parentage. 

"They were also active in a criminal aspect of positive eugenics known as Lebensborn, or “Spring of Life.” Heinrich Himmler had created this institution as part of his plan “to breed the SS into a biological élite, ... [a] racial nucleus from which Germany could replenish an Aryan inheritance now dangerously diluted through generations of race-mixing." Lebensborn administered welfare assistance to SS families in the service of “racially valuable” children, and extended maternity and childcare facilities to married and unmarried mothers. But Lebensborn also engaged in the kidnapping of “biologically valuable” children (those who met Nordic criteria) in occupied areas, some of them fathered by German occupiers. The policy was explained plainly on one occasion by Himmler himself: “I really intend to take German blood from wherever it is to be found in the world, to rob it and steal it wherever I can."

Nazi Doctors, p43.

Now you can understand the context for the Rudolf Hess quote, "National Socialism is nothing more than applied biology."

Why bring up the past?

So we won't repeat it.

We won't repeat the horrors of negative eugenics as long as we view all human life as worthy of life ... regardless of genetic flaws, including Down's Syndrome ... regardless of stage of development ... regardless of our estimation of their contribution to society ... and regardless of our opinion on the quality of their life.

We won't repeat the horrors of positive eugenics as long as we resist the urge to tinker with genetic engineering in an effort to improve the species ... and resist the urge to order designer babies ... and resist the urge to use genetic screening to get the offspring that we truly want.

In the words of Ben Mitchell,

"Only vigilance on the part of all of us can    prevent a bleak eugenic future. The social, ethical, and legal implications    of the new eugenics is not an arena for only the scientist, philosopher,    theologian, or lawyer. We all have a stake in our genetic future."

For further reading on eugenics:

Eugenics in the Springtime by C. Ben Mitchell, The Center For Bioethics & Human Dignity
Hurtling Toward Eugenics... Again by C. Ben Mitchell, The Center For Bioethics & Human Dignity
Eleventh Week Eugenics: The Killing of Down Syndrome Children by Joe Carter, Evangelical Outpost
Answers.com : Eugenics
The Image Archive On The American Eugenics Movement
The Nazi Doctors, by Dr. Robert J. Lifton
Apple Pie Eugenics, Chuck Colson, Breakpoint Commentary, October 2, 2003