Short answers, pulled from the story.
Drang nach Osten is a German phrase meaning "Drive to the East," also translated as "push eastward" or "desire to push east." It originated as a 19th-century German nationalist slogan describing the intent to expand into Slavic territories of Central and Eastern Europe.
The first known written use of Drang nach Osten was by the Polish journalist Julian Klaczko in 1849. Whether Klaczko invented the term or was citing a phrase already in circulation is debated. Because the term is used almost exclusively in its German form across Polish, Russian, Czech, and English sources, scholars have concluded it is of German origin.
Adolf Hitler declared Drang nach Osten an essential element of his plans for Europe in Mein Kampf, published in 1925-1926, stating that eastward expansion was the direction "nature herself has decreed" for the German people. Nazi Germany used the concept to justify Lebensraum, a policy of colonizing Eastern Europe by displacing and genociding Slavic populations through Generalplan Ost.
Generalplan Ost, or the General Plan for the East, was Nazi Germany's plan for total Germanic domination of Eastern Europe through genocide of Slavic inhabitants and forced deportation of survivors beyond the Ural Mountains. It was the administrative implementation of the Drang nach Osten ideology under Hitler's Lebensraum doctrine. The plan began to be implemented in conquered territories including Poland, Belarus, and Ukraine before the Soviet Union reversed German advances in 1943.
Most of the demographic and cultural legacy of the medieval German Ostsiedlung was ended between 1945 and 1948 when Germans were expelled from territories east of the Oder-Neisse line under decisions of the Potsdam Conference. The territory historically called "Eastern Germany" was divided among Poland, Russia, and Lithuania and repopulated with settlers of those nationalities.
Drang nach Westen, meaning "thrust toward the West," was a concept promoted by German nationalists after World War I to describe an alleged Polish drive westward into German territories. It was framed as a mirror image of Drang nach Osten. As recently as August 2002, the Polish newspaper Wprost used both terms in the same issue to describe contemporary German-Polish economic and demographic relations.