The Cold War was a conflict that took place during the second half of the 20th century, between the Eastern bloc constituted by communist countries under the leadership of the URSS and, on the other side, there was the Western bloc of capitalist countries leaded by the US.
Both the US and URSS had nuclear weapons. After the disaster caused by the nuclear bombs that the US threw over Hiroshima and Nagashaki at the end of WWII, none of the confronted parties wanted to start a nuclear conflict, because it would bring total destruction for the two of them (and for the whole world). Instead of starting a direct conflict, the US and URSS became rivals when they supporting opposite sides in the many so-called proxy wars: Korean War, Vietnam War, Cuban conflict, etc.