The Berlin Airlift helped achieve American goals in postwar Europe by proving to the Soviet Union that the US would not back down on the issue of Berlin and by pushing West Germany much more firmly towards alliance with Western Europe and the United States.
In postwar Europe, the US wanted to prevent any expansion of the Soviet bloc that existed in Eastern Europe. In order to do that, the US had to convince the Soviets that they would defend Western Europe. The US also had to convince the countries of Western Europe that an alliance with the US was in their best interests. The Berlin Airlift helped with both of these things. It showed the Soviets just how determined the US was to resist communist expansion. It also showed the West Germans that the US would stand up for them and help them. This proved that there were benefits to alliance with the US.
In these ways, the Berlin Airlift helped to achieve US goals in postwar Europe.