The support of West Berlin was part of the political approach that the US had estaliblished at the moment: the policy of containment against communism.
After the Postdam Conference, Germany was divided in four occupation zones, the three Western ones were under the control of the Western allied powers and were unified under the name of Federal Republic of Germany, while the Eastern ones pertained to the URSS and constituted the German Democratic Republic. Berlin was embodied within this fourth Eastern zone, although the city itself was divided in four zones exactly in the same way as the whole country. Therefore, West Berlin was a small area under the influence of the western Allied powers (US, UK and France) embodied in URSS territory.
When the US directly declared their absolute support to West Berlin, it was a clear proof of the contaiment policy that aimed to block the spread of communism and of the confrontation attitude that characterized the whole second half of the 20th century that constituted the Cold War era.