The main idea of communism or socialism is that individuals do not exist for their own sake, rather, they exist for the sake of the state, the group, the race, or "society" in general. The opposite is capitalism, which is the idea that every individual has the right to his own life, liberty, and pursuit of happiness.
In practice, communism means the government can tax the hell out of you, regulate prices, interest rates etc., control what you do (banning alcohol, smoking, transfats, prostitution, abortion, etc.). In practice, capitalism means the fruit of your labor belongs to you, and you alone are in control of how to dispose of it, and you can do anything you want as long as all involved parties consent.
Today, both republicans and democrats are socialists: they argue about how the government is going to control your life, but they don't argue about whether it is right for the government to control your life in the first place.
People like to accuse their enemies of being "communist" because it is obvious to everyone that the most communist countries are brutal dictatorships. The funny thing is, they are just as communist, they just convince themselves that somehow, their version of communism will "work out" even though it has failed repeatedly throughout history.
http://www.aynrandlexicon.com/lexicon/communism.html
http://www.aynrandlexicon.com/lexicon/capitalism.html
http://youtube.com/watch?v=mWv5VZWlwRQ