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After World War II, four allied powers divided Germany into four occupation zones. The American, British, and French zones became the Federal Republic of Germany (BRD/FRG, West Germany) and the Soviet zone became the German Democratic Republic (DDR/GDR, East Germany). Berlin had a special status, and it was itself divided into four sectors. The three western Sectors were not quite part of the Federal Republic, not quite apart from it. For instance, there was no draft into the FRG army, and the allied commanders were the supreme authority.
At times, the Soviet Union and the GDR government (which took Soviet orders in this regard) tried to blockade West Berlin. The most famous event was the blockade which led to the Berlin Airlift. Other events happened 1958 and 1961. The US appeared ready to defend West Berlin, potentially starting World War III, and the Soviets never quite pushed that much.
Some highways, rail lines, rivers/canals and air lanes were designated as transit lanes, with visa-free travel. This was improved in a 1972 treaty. The GDR earned money from transit fees, so it was in their interest to promote travel. Of course they were also afraid of East Germans trying to escape, and West Germans telling the Easterners what Communists did not want them to hear.
That being said, the civilian access to and from West Berlin was never quite as secure as the access of the Western Allied military. The government of Berlin maintained the Senatsreserve, a stockpile to hedge against another blockade. And some Germans would fly to the West rather than take a car.