What is an IP PBX?
An IP PBX is a telephone switchboard which uses IP (the Internet protocol) to carry telephone calls over computer networks instead of using the PSTN (the regular phone network) and traditional phone lines (ISDN or analogue). Telephone extensions on a traditional PBX are connected using regular analogue connections (phone sockets) with each socket being wired back individually to the PBX. An IP PBX doesn't use phone lines (analogue/ISDN) to connect to the PSTN but instead uses the Internet (or sometimes a private IP network) to connect to a PSTN gateway (IP Trunk).
An IP network uses your existing Ethernet (CAT5/UTP) within your premises. Once your IP PBX is installed onto your network, your IP telephones can communicate with the PBX by plugging into any of your network sockets, in the same way that you can plug in any computer. You do not need specific extension sockets so installation is much simpler and more flexible as you can move an extension just by plugging it into a different socket (an extension's identity is determined by the phone's settings, not the socket it is plugged into).
IP, being the protocol of the Internet can be passed directly onto the Internet using your broadband line or other Internet connectivity so if you have an IP phone plugged in somewhere else on the Internet (anywhere in the world) that phone can connect to your PBX and call to/from the IP phones in your office.
Of course, until the whole world uses IP, most of your calls will still be to or from the regular telephone network (PSTN) so you need a method to call to/from your IP network. On a pure IP PBX, there are no analogue or ISDN trunk lines; the IP PBX has no direct connection to the PSTN, just a connection to the Internet. You therefore need to use a PSTN gateway - this is a server which interconnects your IP network with the PSTN so that your outbound calls can be passed onto any regular phone number and you can have a regular PSTN phone number which routes into your PBX. This service, or provision is called a VoIP Trunk (or a 'SIP' trunk as SIP is the signalling protocol used).
The following two diagrams show the topology (the connection relationship of all components) in firstly a traditional PBX and then an IP PBX:
Above is traditional PBX. For every line, you need another connection into the PBX from the outside world, so line rental costs and for every extension, you need another dedicated cable all the way from the phone back to the PBX. This means a lot of wiring, and therefore difficult to change later. Traditional PBXs are also generally much larger physically.
With an IP PBX (above) you use your existing computer network, so only one connection is required back to the PBX. SPlitting anywhere along the way with additional Ethernet switches as required. A DSL trunk (your connection to the outside world) replaces all of your multiple incoming lines.
This has been just a very brief introduction to the key operational theory of an IP PBX. You can learn more about PBXs here.