The Wired is an internet-like communication system used by the majority of the Lain cast.
"There is the world around us, a world of people, tactile sensation, and culture. There is the wired world, inside a computer, of images, personalities, virtual experiences, and a culture all of its own."
The Wired is "...An advanced form of communication." where people all around the world link to share thoughts, conversation, play games, and socialize. It has become such a meaningful and useful tool in modern society that modern society would almost cease to function without it. I guess you could call it a 'religion' of sorts, as people tend to worship it giving the Wired top priority in their daily lives. Many older citizens of society feel that there is a danger to the Wired. It, while being a very useful tool for life, can also become an obsession to those who do not secure themselves in the reality that no matter how real the Wired may be the true world will always be more real. (Source )
The Wired is assumed to have run mainly IPv4 and IPv6 previously to the attempted upgrade to IPv7.