#bellcore

When you dialed a rotary phone, it triggered these electromechanical crossbar switches, known as a Strowger crossbar, at your local exchange (LEC), which would connect through to the number (at another exchange, or through an intercity / long-distance exchange).

If you have an older, low-profile building in your neighborhood with no windows and maybe a phone company logo on it, that's a local exchange. They were filled to the brim with these switches, cables, electrical gear and cooling equipment. Nowadays, they've been mostly emptied out, and if still in use, hold some standard 19" equipment racks with modular network-switching gear linked by Ethernet cables, just as you might find in the server room of your office's IT department. Not only are they your telephone exchange, they're also your local connection to the Internet, if you have a DSL modem.

Some companies rent and co-locate web servers in these spaces, in order to push content closer to consumers and avoid delays (known as a content delivery network).

But back to phones:

Local exchanges served up to 10,000 lines; In the US and Canada, the exchange number was the first two or three digits of your phone number, and your line number was the final four. In the early days, they'd give exchanges handy mnemonics that translated numbers to letters, so you could dial "CHesterfield 3-4567."

Crossbar switches replaced and automated the old process of manual call completion by operators. Early phones had no dial, you had to ask someone to connect you, and likely, they had to ask another operator to patch you through, so on down the line. 

By the 1960s, crossbar switches and electro-mechanical dialing were slowly replaced by electronic, and later digital, switching and connection systems. Cities were connected first by massive trunk lines, and then by the 1980s, by fiber-optics. 

The operating system UNIX (formally known as System V) was created at Bell Labs to run these digital switches (the ESS series of Electronic Switching Systems), which in their early incarnations, still used electromechanical relays and reed switches to connect calls, running at a mighty 1MHz, with 140-lb hard disks for recording data. Some of those first-generation switches are still in use in some southern states and smaller cities. 

(The ESS and UNIX played a central role as the MacGuffin in the so-called 'Hacker Crackdown' of the early 90s, described by Bruce Sterling in his book of the same name; a section describing the trial of Phrack publisher Craig Neidorf, accused of publishing purloined documents from inside Bellcore, is here at MIT)