Condo-Chicago building built in the 1920’s. Is this some kind of tube to communicate to the lower floors? I am not sure what the button is for either, it was pushed but we did not hear anything. Looked all over the place including the common areas and did not find anything else that was similar.
Its an old fashioned intercom
Had one in my place growing up.
That’s how I met the pretty girl living upstairs 
Correct.
A person at the front door would ring your apartment. (Button located at mailbox).
You would ask “who’s there”?
They would answer “It’s me”!
If you wanted to let them in, you pressed the button to unlock the door, so you didn’t have to go down to the door to open it.
I seem to recall a lack of privacy with those.
One giant party line.
If memory serves me correctly, they did not go to electric/speakers until the 60’s or 70’s. And usually only then for new construction. They didn’t bother converting the voice tubes, because they worked so well, and due to the expense of wiring the system.
That even a fancy one with door button
People used to paint them and make the speaker look like a mouth.