Comment by immibis

It's ISP←A→Telco←D→Telco←A→You

Traditionally both the ISP and you pay for analog phone lines from the telco. The telco uses digital internally (remember you and your ISP probably aren't at the same exchange), which puts a hard limit on data rate - there is no trick you can do to get more bits through than the bits used in the digital part of the call.

If you (as the ISP) buy enough lines you can get them delivered in digital format. A T1 is designed to carry 24 simultaneous phone calls, acting virtually as a bundle of 24 analog phone cables. So the obvious next stage was to have a modem that can handle 24 simultaneous connections on one cable.

Now you have ISP\_modem←Ax24→ISP\_muxer←Dx24→Telco←→Telco←A→User

The ISP's modem generates analog signals for up to 24 simultaneous incoming calls, and they pass into a multiplexer that connects 24 analog lines to a T1 line and they go through the telco digitally to users. The maximum bandwidth is still as before - the modem has to generate an analog signal that will still be receivable at the other end after A2D and D2A conversion. Even though the digital bandwidth for the digital part is 56kbps, the maximum achievable bandwidth through this digital-bottlenecked analog call was found to be 33.6kbps.

But the industry had an idea: by convincing the telco to install the modems into the user's exchange, the analog portion would only be between the telco and the user, without a digital segment in the middle of it, and therefore wouldn't be bottlenecked the same way. The same digital backhaul from the ISP through the telco was used, but instead of transmitting a digitised analog modem signal and therefore causing degradation of quality, it transmitted your actual internet traffic bits, up to 56kbps. The analog signal was made at the user's side of the telco and didn't have to fit within 56kbps when digitised.

Pedantically, the digital circuits are 64kbps but one bit in some bytes is used for call status signaling, which is okay for voice, but the ISP equipment can't predict which bytes have a bit overwritten (and it could be multiple if there are several hops) so it just used 7 bits in each byte.