PBX stands for Private Branch Exchange, which is a private telephone network used within a company.
Traditional PBXs would have their own proprietary phones, such that there would be a way to re-use these phones with a different system. This means that we either have system-lock-in (we are bound to the same system because changing system means also changing phones, which makes it prohibitively expensive to break away) or vendor-lock-in (we are bound to the same vendor because the phones are only usable with systems from the same vendor, sometimes only within a particular range of systems).
Time and Technology however have changed the consumer telephony landscape, with the flag-bearer being the Open-Standards-based IP-PBX. The point of the “IP” in this new era is that the phone calls are delivered using the Internet Protocol as the underlying transport technology.