A PBX (Private Branch Exchange) is a small telephone switch owned by a company or organization. An IP PBX is simply a PBX which supports VoIP (Voice over IP). An IP PBX can also be referred to as a VoIP PBX.
An IP PBX may support VoIP both internally and externally. Internal VoIP support means that the IP PBX uses VoIP to communicate with each of its connect PBX phones. External VoIP supports means that the IP PBX uses VoIP to route calls to the outside world.
Most IP PBX's also support older analog or digital PBX phones and also support external connections on the public switched telephone network (PSTN).