The black cord has no real importance to the plot of the book. That cord simply represents the dark ones power flowing to the chosen. It doesn't affect the plot and is simply a tool that Robert Jorden used to help describe what was going on. (We didn't even know how the power worked at that point, remember) The cord isn't any different from the glow around Aes-sedai. The difference is that the power is everywhere(hence the glow) and the dark one is restricted to a certain point (hence the cord). I really don't understand what the deal with this is.