This continues on from the Evolution of Telephony post.
An IP PBX connects internal telephone calls and connects outgoing calls to the public switched telephone network over a data connection using the Internet protocol.
IP PBX is the next (and current) evolution of PBX. It stands for Internet Protocol Private Branch Exchange. Some folks call it IP-based PBX as well.
As we move further away from our humble, person-based switch boards, we more towards more automation and tighter integration with all communication channels. With IP PBX we no longer have two lines of communication entering the office - voice and data. We combine the two one telecommunication line and run voice and data over that line (aka VoIP). The IP PBX takes the voice data and redistributes it to the appropriate phone, like traditional PBX systems.
To recap traditional PBX systems: A PBX is a telephone switching system that connects numbers within the private branch and connects the private branch to the public phone system.
IP PBX switches voice information over the Internet instead of the traditional telephone system. People have moved to IP PBX for many of the same reasons as the move to PBX - it's cheaper and more efficient. With IP PBX you do not need to maintain separate data and voice lines. Startup and maintenance costs are lower; instead of specialized equipment, IP PBX systems can be as easy as a piece of software. Of course, the larger your organization, the more complex your IP PBX system is.
The systems can perform the same tasks as the traditional PBX systems. You can probably get more functionality than traditional PBX systems for comparable amount of money. Typical functionality includes extensions, voice mail, call-forwarding, call-holding, call-parking, and conferencing.