Private branch exchange is a phone system that allows you to connect all of the phones in a building. Users of the system can dial internally or externally using shared phone lines. In the original case, the PBX was not a thing but a switchboard operator. It was a person with plugs who would connect your extension to an outside line. Well, the PBX automated all of that work that a switchboard operator would do. It would allow you to dial internally or externally with the PBX in place. Businesses could have a ratio of external lines to internal lines.
A Real World Example
Let's explore an example of a business that has 100 employees. The business is only ever going to have ten of their employees talking to the public network, so now with a PBX they would only paying for ten lines instead of paying for 100 lines. All the calls internally are now free because they're going to the PBX. Then the business can start adding things. They can have push to page capabilities. They can page everyone in the building or page people individually. All that stuff started to get added but the reason to have it there was you needed a way of bringing together, connecting together all the phones in a single building. Over time, PBXs got bigger and bigger because organizations got bigger. Sometimes, they started to span locations so you'd have a PBX here and a PBX there and you'd have private connectivity between them to create an organization view of the PBX. One employee might be sitting in Los Angeles. Another might be in Boston. They could internally dial to each other but it wouldn't be going out to the PSTN. They would have private connectivity between the businesses.