Lain's abilities/plot: The way that they are supposed to work is that she was the avatar corporeal form of the 7th protocol that had complete control over the "wired"(the internet) at the same time that the wired became powerful enough and flexible enough to interact with the electromagnetic field of the earth. Basically Lain is a software program that had complete control of the internet and was able to downloaded itself into the earth's magnetic field. How her powers work in the real world is less clear. The way the series explains it, she should be able to control the minds and memories of all living creatures, as well as having significant control over the earths EM field and naturally resonant sound waves. This included, but was not limited to, making a body in the real world that could interact in a real way with people.