A PBX is fancy way to say "business phone system". It is a telephone switch that you own or lease. Basic features of almost all PBXs include conference, transfer, hold, calling groups, caller ID, redial, speed dial, call forwarding, and various forms of call coverage. Advanced features can include call answer and voicemail service, automated attendant, call queues, unified messaging, call accounting, call center applications, and networking.
PBXs are connected to the outside world or PSTN (public switched telephony network) through your demarcation point (demarc) to the local telephone company or service provider. Wiring is also installed throughout your building so that telephone extensions can be connected to the PBX. In this way users can call other extensions connected to the phone system and can also take incoming and make incoming telephone calls.
Most of today's business phone systems can accommodate analog, digital, and IP lines as well as analog, digital, and IP telephone stations. They also have robust voicemail, networking, and unified messaging features. While there are a large number of PBX makers and a competitive market exists, major manufacturers include Avaya, Cisco, and Nortel.