In communist philosophies, private property refers to productive tools/resources (""the means of production""), which require inputs from multiple people (the ""working class"") to produce outputs that are claimed by its owners (the ""capitalist class""). Examples: land, factories, businesses.
This is distinct from personal property, which refers to personal possessions such as your clothes, car, and even your house, which are not used to produce outputs.
Anarcho-communism abolishes private property, but retains personal property and collectively-owned goods and services. It also abolishes the state/government. Instead, systems of production and distribution are managed voluntarily by their participants. Each individual and group is free to contribute to production and to satisfy their needs based on their own choice.
Example: The Korean People's Association in Manchuria (KPAM, 1929-1931) was an autonomous anarchist zone, populated with 2M people and operating under a gift economy and mutual aid. KPAM was successful in its endeavours on collective agriculture and free education, and was entirely capable of self-governance. The Korean anarchist experiment was only put to an end by external invading forces.