A PBX (Private Branch Exchange) is a switch station for telephone system. A PBX that is specifically made for VoIP is called an IP PBX.

An IP PBX is a business telephone system designed to deliver voice over a data network
Interpreted with normal PSTN. Adding, Moving and removing users to & from a telephone system can be very costly, but with an IP PBX it is as cost effective as it is easy. Moreover, an IP form my not necessary attached one specific user.

Users can transparently login the system through any phone in the network; without however losing their personal profiles and configuration.