Then what does Communism even <i>mean</i>?
There are plenty of definitions of communism. The Marxist definition excludes what is often called "Communism" in the West, for instance. The latter is most accurately described as Stalinism, since it departed greatly even from Leninism and Bolshevism, becoming almost the opposite of original Marxism. (Some authors prefer to refer to Marx's ideas as "MarxIAN" rather than "MarxIST", since the latter is widely taken to denote a quite different set of ideas).
The basic principles that one might consider "communistic" might be
1. Genuine egalitarianism; hence, not just fictitious nominal legal equality but some degree of economic equality, eliminating the ability of individuals to amass unearned wealth and undue power.
2. Community control of the major elements of production, and of the distribution of, at least, necessities of life.
3. As an adjunct, the communist society will have limited tolerance for disruptive individualism.
These factors work together; you cannot have real community control if a few individuals exercise the real power, and you cannot have a fair distribution of wealth and power without community control.
Many tribal societies may be seen as communistic. The chief and the medicine man may be more influential, but they have very limited means to persuade the tribe to do anything it doesn't really want. There is very little surplus wealth, so accumulation is not a problem. The tribe's way of life and productive roles are well established and cooperative; no one goes against the group consensus because they can't survive unless they stay with the tribe and cooperate. No one is willing to let his neighbor starve to death because every tribe member is needed, and besides they all know each other well.
Larger and wealthier groups do not fair so well with communism, for obvious reasons. The only ones I know of that have succeeded to any degree relied on strong religious conformity (see principle 3), although secular ideologies have been proposed as a substitute. In any case, the larger and richer a communist society is, the harder it needs to fight for conformity.