What they mean is that electrons can be thermally excited into the conduction band. For an insulator, the band gap is so large that thermal excitation into the conduction band is not possible. For semiconductors, the fermi level lies within the band gap. At absolute zero, there would be no conduction at all since no electrons would have the energy to be in the conduction band. But at room temperature a small amount of electrons are excited. The amount of excitation can be determined by the Fermi-Dirac equation. For conductors, there is no gap, and there are always electrons populating the conduction band. I think the confusion comes from the fact that the "possible to excite electrons" statement is vague. A better way to say this is if, at a given temperature, the thermal energy is enough to excite electrons into the conduction band (i.e. Smear the Fermi-Dirac distribution enough that there is some population in the conduction band) then it will conduct. Population of the conduction band is what is important, the textbooks are only discussing in which situations population occurs (small bandgap, high T). The wave functions don't look all that different for a valence band and conduction band electron. The wave functions in a periodic system are Bloch functions. As far as a physical representation of conduction within a QM framework, that's where my brain starts to hurt. I've tried to think of a way to think of this many times before, but since we are not dealing with classical particles it is difficult (maybe impossible) to come up with a visual representation. If anyone else has a good way to visualize this then I would be grateful as well. I I'm wondering if looking at the evolution of the electron density over time would yeild any interesting results. I did something similar with a carotene-porphyrin-fullerine molecule once where we simulated a laser excitation on the porphyrin and calculated the electron density as it moved along the molecule. Anyway I hope this helps a little. It's kind of late so I apologize for the haphazard organization and poorly phrased response.