(covers information from several alternate timelines)
Communism is a political and economic ideal and philosophy that was embraced by several Earth nations in the 20th and 21st centuries. The pillar of the Communist philosophy was equality and pre-planned economy. Nations that embraced it included the Soviet Union and China. Slang terms for a person who followed this ideal, better known as a communist, included "pinko", "red" and "commie." It was the clash between communism and capitalism that drove the Earth Cold War.
In 2364, Q adopted the guise of a United States Marine Corps captain and cynically suggested that the USS Enterprise-D "go back to your world and put an end to the commies". (TNG: "Encounter at Farpoint")