A PBX is a Private Branch eXchange.
Did you ever dial 9 on your business phone to get an outside line?
That’s a PBX!
It’s a device – typically physical hardware like a PC – that hooks up to both phone lines from the phone company and the phone lines inside your office. But with modern phone equipment dialing 9 is largely done away with – the phone can be programmed/configured better than that.
UPDATES - circa 2010-2015…
With Voice over internet Protocol (VoiP), your Ethernet data lines can now do the work that only voice telco lines used to do, with much less wiring.
Today, if you opt for a virtual machine, then with the right telephone company, your PBX services can live almost entirely in software!
UPDATE - November 2020…
The recent 10x increase in Work From Home users showed the rise of the video chat PBX experience – one of many scenarios where no phone lines are even needed! – but you might still call it a PBX under-the-hood because many people still call in from their audio-only phones :) – read more discussion on the evolution of the PBX in this other recent FAQ post.