A private branch exchange (PBX) is a telephone exchange that serves a particular business or office, as opposed to one that a common carrier or telephone company operates for many businesses or for the general public.
A private branch exchange (PBX) is a telephone exchange that serves a particular business or office, as opposed to one that a common carrier or telephone company operates for many businesses or for the general public.
PBXs make connections among the internal telephones of a private organization—usually a business—and also connect them to the public switched telephone network (PSTN) via trunk lines. Because they incorporate telephones, fax machines, modems, and more, the general term "extension" is used to refer to any end point on the branch.
Initially, the primary advantage of PBXs was cost savings on internal phone calls: handling the circuit switching locally reduced charges for local phone service. As PBXs gained popularity, they started offering services that were not available in the operator network, such as hunt groups, call forwarding, and extension dialing. In the 1960s a simulated PBX known as Centrex provided similar features from the central telephone exchange.
Two significant developments during the 1990s led to new types of PBX systems. One was the massive growth of data networks and increased public understanding of packet switching. Companies needed packet switched networks for data, so using them for telephone calls was tempting, and the availability of the Internet as a global delivery system made packet switched communications even more attractive. These factors led to the development of the VoIP PBX. (Technically, nothing was being "exchanged" any more, but the abbreviation PBX was so widely understood that it remained in use.)
Source, and more information can be found at the Wikipedia page on business telephone systems.