The Berlin Airlift was used during the Cold War to resupply West Berlin at a time when it was being blockaded by the Soviet Union.
After WWII, Berlin was split up between the Russians, who had what was called East Berlin, and the Western Allies, who had West Berlin. Germany as a whole was split up in the same way. The problem was that Berlin was deep in East Germany, so there was a part of West Germany (West Berlin) far inside East Germany.
The Soviet Union wanted the West out of Berlin. So, at one point in 1948, it stopped all land traffic to Berlin from West Germany. This meant people in West Berlin could not get supplies. However, the US and the British chose not to leave Berlin. Instead, the used airplanes to ferry in all the supplies that were needed, with the record delivery being a day on which almost 13,000 tons of supplies were flown in.
Thus, the Berlin Airlift was used to resupply West Berlin and, thereby, to ensure that it would remain a part of West Germany.
Although pohnpei has adeptly answered the question already, perhaps I can put a few more details in for you. Yes, the Berlin Airlift was actually a move against the Soviet Union by supplying West Berlin with what it needed during the Cold War.
When Germany was split into the "East" and the "West," it was Berlin that became the focal point in that the "line" ran right down the middle of the city: East Berlin being controlled by the Soviet Union and its comrades and West Berlin controlled by the Western Allies. The Soviet Union was sick of the Western Allies helping West Berlin, so at one point in the late 40s, they stopped all traffic into Berlin from Western Germany. The response of the Western Allies was simply to fly supplies via aircraft into West Berlin! I guess you could say that the response to the Soviet "Berlin Blockade" was the Western "Berlin Airlift." Wikipedia says it nicely:
On 30 November 1945, it had been agreed in writing that there would be three twenty-mile-wide air corridors providing free access to Berlin.Additionally, unlike a force of tanks and trucks, the Soviets could not claim that cargo aircraft were some sort of military threat. In the face of unarmed aircraft refusing to turn around, the only way to enforce the blockade would have been to shoot them down. An airlift would force the Soviet Union into the position of either shooting down unarmed humanitarian aircraft, thus breaking their own agreements, or backing down.
In other words, there was still "free" air space over Berlin, and the Western Allies took advantage of it! The Soviet Union couldn't peg cargo aircraft full of food and medicine as a threat, so their only choice would be to allow it through or to shoot it down (which would be an act of war). The result was just what the above paragraph suggests: the Soviets had to back down because of the Berlin Airlift.
Thus, the Soviet Union's plan for West Berlin to "cave" didn't work. The Western Allies stayed in West Berlin and in Western Germany. And, of course, eventually, the Berlin Wall came down and the Cold War ended.
Overcome ablockade created by Soviet Union