From aa-asterisk.org.uk wiki
A Private Branch Exchange (historically also known as a Private Automatic Branch Exchange) is a cut-down version of a telephone exchange that is often used in offices or large residential establishments. These are usually privately owned (compare Centrex) and come in many different types, shapes and sizes.
Each PBX usually comprises a number of extensions. An extension is traditionally a physical telephone, but modern PBX systems run by computers allow much more flexibility. Typical extension numbers are two, three or four digits depending on the size of the PBX system. Calls may be made between extensions by dialling the extension number on the telephone. External calls to the PSTN network are usually available, typically by dialling a prefix digit followed by the PSTN number.
Traditionally, PBXs were linked to the analogue telephone network using a number of individual analogue lines, but modern PBXs are usually linked to the PSTN by means of ISDN lines, either BRI or PRI. Increasingly, as PBXs are now being implemented in software such as Asterisk, sometimes links are made via VoIP to an interconnect which converts VoIP to TDM. In this calls are typically delivered to the end customer over the Internet or other IP-based network. Similarly, PBXs can also be linked together using similar technology between different customer sites without using the PSTN to call between them.