It is a PBX. They came in all sizes. They were built by Western Electric or Automatic Electric. They had incoming lines & extensions. The operator would answer incoming lines by taking a cord and plugging into the hole that was ringing. she would take the other cord and plug it into the requested extension. She would hold down the ring lever and it would ring. When the person came on the line she would center her key and go on to other calls. When the party hung up the light would start flashing and a buzzer would sound. She would then pull both cords out and they would retract back into the board with just the tips showing, like in the picture. These were used at offices, hotels, hospitals, etc.

These were not what they used at the phone company, when there were operators. Their boards were set up in the same way as far as the cords were but were bigger in scope. They had all sorts of lines beside incoming or out going. There was,Toll Test, Verifying, timers for "time & charges requests, the list goes on. If you wanted a mobile number they had to put you through to that operator and you had to tell them the number "JL 14543" and in the vicinity of where the mobile was. Also had a special operators to make 3 way or conference calls. They made person to person calls to and from operators in different towns and states. This was all before area codes and just 7 numbers. All phones used to have say, GLenwood 4-3678.
The SP was DOuglas 2-1212 in the City. At one time, the SP had the largest privately owned phone company in the world and it made AT&T nervous. They watched the SP and others to make sure they were not cutting them out of toll charges.

Nudge