I really don't know. I see it a lot in some of the articles I read and in each it seems to mean something different. Primarilly it is used as something being denied to to a religious group. A voice in the public square - a place in the public square - access to the public square. Is it the "halls of government", a "soap box" in a public park, a place to erect the ten commandments, a battlefield of ideas - what is the public square? Let me do some "Googling".
Well, if the public square is where the citizens of this great country meet, then that could easily be a privately owned shopping mall. Shopping malls usually frown upon proselytizing on their premisses, don't they?
I seem to recall hearing of some Christians who were complaining that they didn't have access to shopping malls for proselytizing. I wonder if that could have anything to do with this?