The Cold war was a global conflict that was fought between the United States and a capitalist democratic thought against the Soviet Union, with it's ideals of socialism.
It was brought about due to the growing conflict in the post-World War II era when only two super powers remained on earth.
Both countries wanted to exert global influence and since both had Nuclear Weapons, there were very few chances of direct conflict.
Hence, the war was fought trough proxies around the world. If a government was allied with one party, the other country would fund opposition rebels to overthrow the government.
This was played out extensively in Korea, Vietnam and Cambodia, where US funded and Soviet funded militias fought bloody battles. In all these countries, Communist rebels had become extremely powerful.
In Vietnam, the US even sent in direct forces to curb the growth of communist rebels.
Korea was divided with North Korea being pro-socialist while South Korea siding with the United States.
When the dust settled, borders had changed and millions had died.