This basic PBX IP diagram will help many people see how VoIP actually works. A PBX (Private Branch eXchange) is nothing more that a technology that connects more people and devices to the PSTN network than there are actual outbound phone lines (trunks).

The center of an IP based PBX system is Asterisk. It is an open source software that most commonly runs on Linux. The phones all connect to the same network as the IP PBX, and communicate with it. The PBX in turn connects the devices to the PSTN network either through standard POTS lines with zaptel hardware, or directly to a VoIP provider via SIP trunks that in turn terminates to the PSTN network.