Private Branch Exchange (PBX)
A private branch exchange (PBX) is in short, a business telephone system, consisting of multiple lines. PBX's differ from traditional telephone exchanges that serve the public in that a private branch exchange only serves a particular business or office - it is not a publicly shared phone system. Extensions refer to any end point on the public exchange branch - when you call into a business and are asked to enter an extension, they are using a PBX.
In addition to traditional PBX systems, there are hosted PBX system and mobile PBX system.
A Hosted PBX delivers the functionality of a traditional private branch exchange as an actual service, over a normal Public Switched Telephone Network (PSTN) - hosted options are provided by telephone companies using equipment that is a part of that companies exchange.
A Mobile PBX sets mobile phones and smartphones as extensions which allows them to utilize features offered by a traditional PBX.