It says that the energy of the EM wave decays rapidly if it travels through a good conductive material. Therefore, much of the wave is travelling on the surface of the copper wire. (since it decays rapidly if it travels downward and toward (z-direction in the figure) the core of the copper wire).
But this doesn't make sense. Even if the EM wave is travelling on the surface of the copper wire, it is still on the copper medium. This means that it couldn't travel a distance longer than a few "skin-depth" distances even at the surface (x-direction in the figure).