There are at least two ways to look at the importance of Berlin.
First, Berlin was important because it was a constant point of contention between the communists and the West in the first two decades or so of the Cold War. This was true because of the fact that Berlin held an anomalous position. Berlin was deep within the Soviet sector of Occupied Germany and, later, of communist East Germany. At the same time, half of the city was the territory of the Western allies and, later, of democratic West Germany. Thus, West Berlin was a Western enclave within the communist bloc. This made it a source of constant tension, leading to such things as the Berlin Airlift and the Berlin crisis of 1961.
Second, Berlin was important because it was a symbol of the commitment of the West. This is seen most clearly in President Kennedy’s “ich bin ein Berliner” speech. To the West, Berlin was a symbol of how the forces of freedom and democracy were committed to standing up against the forces of communism. This is why Kennedy argued that all Westerners identified themselves with the people of West Berlin.
Belin was important during the Cold War because it was used to show Western powers' commitment of money, time, and resources to rebuilding Europe and stopping the spread of Soviet communism. This was evidenced by the creation of the Marshall Plan.
Later, American leaders began to fear that if Berlin fell, the cities and countries around it might fall. This fear is known as the dominoe effect.