One short term effect of the Manhattan project was the developing of atomic bombs that were used on the Japanese cities of Hiroshima and Nagasaki. The dropping of these bombs helped bring an unconditional surrender from Japan, officially ending World War II.
A long term effect of the Manhattan project is the increased amount of focus and military spending by nations all over the world. This included the Soviet Union, as the United States faced off against the Soviets in what is now known as the "arms race." This was essentially a race of who could develop the biggest and best military weapons to be used in case fighting broke out between the two nations.