TLDR: Germany was the only (populated) place in Europe with a hard border between Eastern and Western Blocs.
At the end of WWII, the Soviets and Western allies each occupied one side of Europe. A number of agreements (the percentages agreement between Churchill and Stalin, British notes seen here, for example) were made that were finalized with the delineation of occupation zones (British, French, American, and Soviet) at the Potsdam conference just after the war's end.
Remember that just before and during the war, Germany had annexed a number of territories (the Danzig corridor, Austria, the Sudetenland), so the areas that had to be occupied were not limited to modern-day Germany. East and West Prussia were annexed by Russia (Kaliningrad Oblast) and Poland, with the remaining German population largely being expelled as agreed in the Potsdam agreement. The Soviet occupation zones of Germany and Austria included Berlin and Vienna respectively; these cities were also divided between the four former allies. Austria, unlike Germany, was not divided into two countries; when the occupying armies went home in 1955, Austria was reunified on the condition that it remain neutral (not join NATO or the Warsaw Pact) and democratic.
Germany, on the other hand, having for the past 50 years been Europe's industrial powerhouse, was a more contentious matter. The Western occupation zone included the Ruhr Valley and most of Germany's industry, which the western allies were reluctant to give up. When the western allies made moves to further tie the west to their bloc (for example, by introducing the Deutschmark in 1948), the Soviets responded by closing land access to West Berlin, hoping to force the western allies to either give up West Berlin or otherwise reverse their economic integration with the western zone. When the western allies flew supplies to West Berlin by air instead, the Soviets realized that neither goal would be achieved and lifted the blockade, leaving Berlin, the largest city in East Germany, as a split city for the rest of the Cold War.
East and West Germany (the GDR and FRG respectively) were established as separate countries in 1949 with the official end of the occupation. There were offers for reunification under the same conditions as Austria (most notably the Stalin Note of March 10 1952), but the western allies were reluctant to give up their larger and more valuable section of Germany. By this time, Yugoslavia had split with the Soviet Union, so the inner German border was one of the only borders between eastern and western blocs. This was especially visible in Berlin where, between 1949 and the construction of the Berlin Wall in 1961, ordinary people could walk between NATO and Warsaw Pact countries with little difficulty, and often worked and lived on opposite sides of the border.

There was also a tendency to compare the two; since both new countries were German and were supposedly starting from a similar condition, it was used as an example of the differences of socialist and capitalist economies. Though this is occasionally useful, it must be recognized that the two Germanies did not have remotely similar conditions in 1949. Whereas the United States was untouched by the war and was ready to provide capital exports in the form of Marshall aid (which the East did not receive), the USSR had been subjected to the most brutal war and occupation in recent European history, and demanded reparations (the vast majority of which were paid by the East in the form of physical capital and labor; many German POWs in the USSR did not return home until several years after the war had ended).