Communism is an ideological and a sociopolitical movement. Its aim is to set up a communist society. This society would be based on the common ownership of the means of production and would lack social classes, money, and a state.
Unhistorically, that is how I would say it. It expresses something that could be but is not.
However, there have been "communist" societies. So, ignoring history is sort of ahistorical.
More historically accurate:
Communism has been an ideological and a sociopolitical movement. Its aim has been to set up a communist society. That society was intended to be based on the common ownership of the means of production and was to lack social classes, private property, and impoverished masses. Power was to be held by a dictatorship of the proletariat(non-capitalists). However, all the so-called communist countries have been authoritarian, one-party states or dictatorships that have failed miserably to bring about these goals.
I disagree about the money part; they forget the most important thing: private property
[some Wikipedia entries are truly dreadful; this is one of them.]