To add to what /u/KanzlerAndreas has already noted (specifically that the wall stopped the stream of East Germans from fleeing to the West), the Berlin Wall served another important objective for the Soviet Union, which was to provide Moscow with one more tool it could use in the Cold War with the United States. The Soviet Union had tried and failed to assimilate West Berlin with the Berlin Blockade of the late 1940s. The American-led Berlin Airlift, which bypassed the blockade and ultimately defeated it, represented a well-known victory for the United States not only materially but in undermining the overwhelming prestige the Soviet Union bore after WW2 in Europe. Thereafter, Berlin became a problem for the Soviets and their Communist Allies because people could literally walk from the capital of East Germany into the West Berlin, where they could then freely travel to West Germany. This was the primary reason the Soviets wanted a wall surrounding the West-Berlin enclave.

After the construction of the wall, however, Berlin's role in the Cold War shifted. Certainly the construction of the wall as another major blow to Soviet prestige--no matter how they spun it, everyone knew they needed a wall because East Germans fled to the West and not the other way around. But with the deed done, West Berlin became a problem for the United States, as it represented an ally deep in the enemy's territory which America had committed to protecting. Khrushchev famously noted just two years after the construction of the wall that Berlin was a "testicle of the West" which he could "squeeze" any time he wanted concessions from the United States. The wall flipped West Berlin from a problem for the Soviets to a problem for the United States.