"Land, natural resources, and means of production may for the purpose of socialization be transferred to public ownership or other forms of public enterprise by a law that determines the nature and extent of compensation."
According to this article, the state can take away someone's property-- but it only applies to meadows and forests, coal mines, factories, etc. The state can seize such pieces of a property when a corresponding law requires it. Then, effectively, they will belong to everyone in Germany.
Article 15 has not been acted upon so far. When the Basic Law was established, divergent views about economic policies were controversial. Namely, whether larger companies should belong to a single person or people should be the owners of such enterprises was a subject of fierce debate.