Belonging to the people at large, and open to them. Not the absence of privacy but the presence of everyone.
Latin publicus (of the people, belonging to the state), an alteration of poplicus, from populus (the people); public names a belonging to everyone rather than an absence of belonging to anyone.
Belonging to the people at large, and open to them. The root is a presence, not an absence: public is not the lack of privacy, it is privacy's opposite claim of ownership, held by everyone at once.