I think the hardest thing to wrap our minds around, in understanding the holocaust, is understanding the pre-World War II racist mentality of most of the European and Euro-American world. Most Europeans and Americans believed fervently in eugenics. They analogized human reproduction to farm animal breeding and frankly wanted to cull what they considered "inferior" stock. Of course, each group believed itself to be superior and others to be inferior. The holocaust discredited that kind of racism in the west.
One of the least known but most important events in 20th century German history is Germany's treatment of indigenous people in their colonies. A few decades before the Germans tried to wipe out the Jews, they had tried and almost succeeding in completely wiping out the Hereros in German South West Africa. Many historians (at least those who are acquainted with this episode) believe that the German genocide against the Herero helped consolidate in the minds of the German elites the idea that it was possible to completely wipe out a people. The other European powers in Africa simply never contemplated doing the kinds of things the Germans did in Africa (the Belgians came close, but that was mostly as a result of mind boggling greed, incompetence, and indifference to human suffering, not industrial scale annihilation).
Fortunately for the people of Africa, German's colonies were taken away from them after World War I. Although the British and French were racist also, centuries of contact and experience with other cultures -- from the colonization of Ireland to the management of Caribbean slavery, to the management of world scale empires -- made the British and French much more pragmatic and by the 20th century simply not genocidal in their attitude toward indigenous people.
But the Germans had basically proven that if you put them in proximity with the "other," they would annihilate them. The "final solution" was their recognition that there was an "other" in their midst, and to apply what they had done in their briefly owned colonies, at home.
http://en.wikipedia.org/wiki/Herero_and_Namaqua_GenocideI, the great general of the German troops, send this letter to the Herero people... All Hereros must leave this land... Any Herero found within the German borders with or without a gun, with or without cattle, will be shot. I shall no longer receive any women or children; I will drive them back to their people. I will shoot them. This is my decision for the Herero people. <3>
General Lothar von Trotha's orders to kill every male Herero and drive the women and children into the desert were lifted in 1904 by the Kaiser, but the massacres had already begun. When the order was lifted at the end of 1904, prisoners were herded into concentration camps and given as slave labour to German businesses, where many died of overwork and malnutrition.