Given the importance of work and production in the life of individuals, it is justified to give them some say in the way in which the means of production are used. The owners of the means of production should not be entitled to decide unilaterally on the conditions, organization, purposes, processes and meaning of production. Production is an important part of human life and people should have a say in it.
Concretely, this means a kind of corporate democracy and participation. Communism traditionally proposes common ownership of the means of production. The workers in the factory, rather than the capitalists or the shareholders, would own the factory in common. Or, rather, society as a whole, which in communism means the class of workers, would own the totality of all means of production. This would obviously spell the end of private property, not necessarily private property as such, but in any case private property of the means of production.
This is unacceptable because private property is an important value. It’s unequal distribution should be criticized, as well as the exclusive right of decision of the owners of the means of production, but there are good reasons to keep the right to private property more or less intact (or, more specifically, the right to legal protection of private property and the right to use it freely).
Common ownership of the means of production, as proposed by traditional communists, is not the only means to create corporate participation and worker control over production. Modern-day capitalism has in some cases reconciled private ownership with large measures of worker participation. Many decisions in companies are now taken by the owners and the workers together. This participation is not incompatible with the free market either. A free market is a system between economic agents, not within them.