What was the Cold War?
The Cold War refers to global tensions between the United States (USA) and its allies and the Union of Soviet Socialist Republics (USSR) and its allies. Some of the deeper issues that set the USA and the USSR at odds were that the USA was committed to capitalism and democratic institutions of government, whereas the USSR was committed to communism and imposed authoritarian government. The Cold War was mostly a tension between these worldviews.There were also immediate conflicts and pressure points as the Cold War began. One of those issues was that the USA had atomic weapons and the USSR did not. (The US would not share that technology with the Soviets, who had been their ally in World War II.) When the Soviets developed their own atomic weaponry, this led to a massive arms race between the superpowers, which also was a big feature of the Cold War.
What was "containment"?
The policy of containment focused on keeping communism and the Soviet Union's influence limited, rather than by trying to confront the Soviet Union directly or eliminate communism completely. It influenced US foreign policy by prompting intervention in places like Korea to stop the spread of communism.
George F. Kennan recommended the policy of containment which set the tone for US involvement in world relations following World War II. Kennan was an American diplomat in Moscow after World War II. In 1946, he sent what became known as "the long telegram" of his advice about what the USA needed to do about the Union of Soviet Socialist Republics (USSR). It really was a long telegram -- it totaled 8,000 words.
In those days, everyone feared an ultimate confrontation between the USA and the USSR -- that the Cold War would someday explode into a massive heated conflict between the superpowers. Kennan, in Moscow, had much foresight to see the internal problems the USSR had. He advised not pushing the conflict too much, but instead just try to "contain" the Soviet Union and wait for their system to collapse under the weight of its own problems. Kennan was right. It took almost 50 years, but eventually the communist system in the USSR fell apart. [The Union of Soviet Socialist Republics came to an end in 1991.]