The Cold War was the term given by anti-communist essayist George Orwell to an period of tension between the capitalist and socialist world following World War II.
Origins
The US and more generally the Allied block were content to let the Soviets fight the brunt of the war against Germany and then swoop in to deliver the finishing blow after the two had exhausted each other. Notably, Stalin offered to commit 1 million Red Army soldiers to an invasion of Germany if France and the British Empire followed with their own troops, opening two fronts at once before Hitler had a chance to ramp up the war effort. The Allied powers refused his request, as they had hoped that both would fight each other first.
After WW2, tensions picked back up between capitalists and socialists, and thus the cold war was born. The USSR especially had industrialized rapidly since Hitler's election and was now a world power of its own. As the Red Army were the first into Berlin, which rushed the surrender of Germany, they scared the rest of the Allied powers into increasing their response against the Soviet republics (so as to defeat socialism for the time being and reinforce their bourgeois class privileges in the world).
While bourgeois historians will downplay the criminal acts committed by the Allies (excluding the USSR after 1945), or try to make some false equivalences between the two powers abusing their authority (for example the Afghanistan war of 1978), we know since the opening of the Soviet archives and the declassification of U.S. documents that the Cold War was a front for imperialism and anticommunism, and most if not all international criminal acts were committed by the Allied powers -- such as the Years of Lead in Italy (NATO-funded neo-nazi groups under Operation Gladio committed several terrorist acts) or the Afghanistan war itself (The USSR was asked to intervene against the U.S.-funded Mujahideen by the government of Afghanistan).
Three worlds theory
It is also from the Cold War that the terms first-, second-, and third-world started appearing in bourgeois republics.
The first-world, also called the "free world" by the bourgeoisie, represented the countries aligned with the United States.
The second-world was therefore the countries aligned towards the USSR, and the third-world were the non-aligned countries.
Such distinction was mostly made in the imperial core. Countries such as Cuba considered themselves non-aligned, but were forced to trade heavily with the USSR as first-world aligned countries embargoed them -- which more easily allowed these same countries to later justify military intervention, citing communist ties as a reason for intervention.