Dial-up uses modems on the public switched telephone network (PSTN) using a plain old telephone service (POTS) line.
It has a maximum theoretical speed of 56 Kbps with the V.92 specification, although North American phone systems limited speeds to 53 Kbps.
Dial-up is too slow to browse the web, but it is extremely useful for out-of-band management of routers, switches, and other text-based network devices.
All you need is a phone line and you can dial in to the device.
You may ask why you need it, if you have an IP address configured on the device.
It is often used if the device loses connectivity from the Internet or network and is too far away to drive to. You can just dial in to troubleshoot it.
Dial-up is a backup control for network outrages since it uses the PSTN network for connectivity.