It means the ownership is socialized (owned by the workers) as opposed to owned by capital (owners). If applied to macro like the Communist experiments of the 20th Cent., then clearly they all failed (with the exception of China)
China got where it got today after they essentially allowed private capital ownership in the late '70s when Deng Xiaoping took power and began carrying out significant economic reforms. They switched from a planned economy to a mixed economy with an open market. In short, "Communist" China is as Communist as any other Capitalist country out there...
Ask yourself, would you rather China had not turn "communist"? could the world handle 2 billion Americans more?