Social Darwinism is the belief hat some races are inherently superior to other races. It was a by-product of the nationalism that emerged after World War I and one of its main proponents was Adolph Hitler who believed that Germans were superior to Jews, Blacks, Russians and Slavs. As a result of this fascism, the Nazi party in Germany began to exterminate the Jews in what is called the Holocaust. Hundreds of thousands of Jews were lined up in front of trenches, shot so that they fell back into the trench and then were bulldozed over.
When this proved too psychologically traumatic for the soldiers, Jews from Germany and Poland were taken to concentration camps such as Austritz and killed by the gas chambers. It was Hitlers intention to kill off the other groups and the mentally retarded.
The Germans were not the only ones that held themselves to be superior. Italy wanted to revive the ancient Roman empire ; Japan had resisted cultural and military infiltration up to that point and these three nations joined together in World War II to for the Axis nations
The major impact of Social Darwinism in Europe after WWI was negative. You can argue that the ideas of Social Darwinism helped lead to the ideas of fascism. Fascism, of course, was a major cause of WWII. Thus, it is possible to argue that the application of Social Darwinism led to WWII.
The main tenet of Social Darwinism is that human society, no less than nature in the wild, is the scene of a struggle for domination. In the wild, only the fittest survive. In human society, only the fittest human beings come to power and only the fittest countries are strong on the world stage. If you take these ideas to their logical extremes, they mean that governments should try to weed out the weakest members of their societies (so that their society as a whole can be stronger) and that countries should not shy away from wars (because wars determine which countries are fittest and give those countries greater power in the world).
These ideas were certainly compatible with the ideas of the fascists (of whom the Nazis in Germany were the most prominent). Nazi beliefs in such ideas helped inspire them to do things like sterilizing or even killing mentally ill people or disabled people. The Nazis believed that their race was the fittest race and that they deserved to take things from people who were less fit than they. This can be seen, for example, in the German attempt to conquer the Soviet Union to provide lebensraum for Germans.
Thus, while Social Darwinism did not inspire the Nazis and other fascists, the fascists were clearly in agreement with Social Darwinist ideas. Therefore, some have argued, Social Darwinism helped to lead to the rise of fascism and to WWII.