Private property is a concept used in law. The law says that a single person or a group of people can own certain things and control them. All the things that are not owned by single persons, or a group of people belong to all. That way, a person may own a car, but the park in the city is only administered by the city, and belongs to all people (or to no one at all).
Different schools of thought have different ideas of how private property should be handled.
Private Property in Socialism and Communism- according to Marxist Theory- refers to the means of production such as mines, factories, burger joints, and so on. These are things communists want to be democratically owned by workers. This is different from Personal Property, such as a toothbrush.