The Cold War was a rivalry between the United States and the Soviet Union that took place after WWII and lasted until 1989. Each side thought the other intended to conquer the world with its ideology. The US and the Soviet Union were allies during WWII, but after the Soviet Union continued to occupy Eastern Europe and the US used atomic weapons without formally announcing that it had them, both sides did not trust each other.
The Cold War primarily involved the US and the Soviet Union. Both sides developed atomic weapons and massive armies. The military budgets for both countries was very high--this money could have been spent on domestic issues. Each side demonized the other side, and to this day there is still a distrust among the nations. Both sides recruited allies--the US would form NATO for the defense of Europe and the Soviet Union would create the Warsaw pact in Eastern Europe. In addition to this, both sides would also recruit allies in the developing world and try to prop up governments there friendly to them. The Soviet Union was Fidel Castro's primary supporter and the US backed the regime of Ngo Dinh Diem in South Vietnam before he was assassinated. The Soviet Union and the United States also fought proxy wars in the developing world. The Korean War and the Vietnam War are primary examples of this.
Even today there is a level of distrust between the US and Russia. With a few exceptions worldwide, communism has disappeared. The legacies in the Middle East and elsewhere of the Cold War still affect the world today. The US's backing of a pro-Western government in Iran led to the rise of the Ayatollah Khomeini and anti-American sentiment in that part of the world. America and Cuba have a mixed relationship that has improved only in recent years. Technically North and South Korea are still at war, and this region periodically threatens to erupt in open warfare again.
The Cold War was a global competition between the United States and the Soviet Union. It happened because the two sides had different ideologies and therefore distrusted one another. It had many impacts on the world.
The Cold War involved practically every country in the world. Almost all countries had to take sides. Many countries had fighting occur on their territory. However, the two main countries involved were the US and the USSR as they were the leaders of the democratic/capitalist side on the one hand and the communist side on the other.
The Cold War had many impacts. Let us look at three of them here. One impact was to make the communist countries of the world rather backward economically by the time the competition ended. Another impact was that it created a split world in which practically every country took a side and there was great animosity between the sides. We see this to some degree today with the enmity between the US and Cuba and between North and South Korea. Finally, the Cold War caused upheaval in much of the less-developed world. The US and USSR competed for influence in those countries, often causing or exacerbating civil wars. The two sides propped up dictators and other unsavory regimes in countries that were on their side. These things had very negative impacts on the less-developed countries.