iiNet began offering dialup internet to small groups of customers in 1993 when the technology was very new, however dialup dates back to the 1950's when it was first used for data transmission for the US government (and it was by today's standards, painfully slow).
Dialup internet uses a modem and a phone line to dial in to your Internet Service Provider's modem. Think of this like making a phone call, except data is exchanged instead of words.
Dialup only requires connection to a fixed telephone network, so it's readily available for people living in rural areas where broadband may not be available, travelers, those on a budget or those that don't need a speedy connection. Dialup has a download speed of 56kbps.
Over the last few years, broadband internet has been replacing dialup as an internet connection method as it's much faster. There are some areas still without high speed broadband where dialup is sometimes the only option to connect.