The first IRC daemon was written in the summer of 1998 by Jarkko "WiZ" Oikarinen of the University of Oulu, Finland. Originally intended as a BBS-style replacement for Talk, IRC quickly spread; first through Scandinavian, and then throughout the rest of the world. Within a year there were over 40 servers linked up.
At this stage there was only one network, and so a name unnecessary - it was simply 'IRC'; but as the size of the network grew, disagreements began to form. IRC was a pretty chaotic medium with netsplits, nick collisions, and channel takeovers all commonplace; and it was inevitable that at some stage users would split off to form their own networks.
One of the first major splits was in 1992, when Wildthang created the Undernet network. Originally intended as a test network, Undernet quickly grew, gaining a reputation as a friendly network due to it's introduction of services to protect users and channels.
Two years later, Undernet itself forked, the new networking becoming DALnet. DALnet's founder, dalvenjah, took Undernet's concept of services to a new level, introducing support for nick registration, G-lines, and a host of other features.
Meanwhile on IRCnet (as the original IRC network was now known), feelings where running high. IRCnet was opposed to the concept of channel/nick 'ownership' which Undernet and DALnet had introduced, but clearly something had to be done about the constant channel takeovers that were occuring. Two alternative ideas were proposed: nick/channel delay, and timestamping (see http://www.irc-help.org for information), but there was bitter dispute over which to implement.
In July of 1996, IRCnet split, with most of the North American servers leaving to form EFnet, leaving IRCnet as a mostly European network.
Since then, hundreds of other smaller networks have formed, most using modified versions of either DALnet, EFnet, IRCnet, or Undernet's ircd.