To answer this, we should look at ultimate causes and proximate causes.
The ultimate causes of the fall of communism had to do with communism itself. The communist system was too repressive and too inefficient. It made people very unhappy because it denied them rights. At the same time, it failed to create enough material prosperity to make up for the lack of liberty. This planted the seeds for the eventual demise of the system.
The more proximate causes have to do with a few world leaders. The election of John Paul II as pope helped to weaken communism because it gave anti-communist Poles a rallying point. The election of Ronald Reagan as President of the United States led to an arms race that further weakened the communist system. Finally, the coming to power of Mikhail Gorbachev in the Soviet Union led to reforms that opened the system up a little and led to the fall of communism.