As any other type of accommodation such as hotels are owned by the government, the term 'casa particular' states that this kind of paid lodging is privately operated by the Cuban family living in the house.
Cualquier otro tipo de alojamiento como hoteles, moteles, campings, etc. pertenecen al estado, por tanto el termino 'casa particular' significa que este tipo de hospedaje pagado es operado por 'particulares' o ciudadanos privados.