It would seem quite a simple thing to define, but has many elements in regard of its use, maintenance, control, and benefit to many who use such.
A basic definition would be a place that is open and accessible to the general public. Roads, public squares, parks, and beaches are typically considered public space. Although it’s not commonly thought of, libraries fall under the range of public space, but requiring continual funding and building maintenance, sets them aside to some degree and not thought of in the same realm.
Public spaces do, understandably, require maintenance, and as such an element of control is given to local council and authority to ensure its safety and continuance for all that wish to use it.
As public space is under such control and protection, council can, and do make it available for commercial events which possibly require payment, but moreover as the protectorate, require certain permissions to allow its use.