Directional cables - what does that really mean?

As far as I know it has to do with shielding to minimize interference from other sources and line voltage noise. The shield is only connected at one end to minimize ground loops from one item to the other also.

The electrons go back and forth, at least somewhat and at very low speed, they are virtually standing still, but the signal does not go back and forth. That's the issue. Thus any wire or cable will sound better in one direction than the other. This includes wire inside speakers, wire inside transformers, internal wiring of components, fuses, etc.

but the signal does not go back and forth

Interesting concept. Please define "signal."

Some cables have a gadget, like MIT network boxes, at one end versus another. That would at least seem to have some concrete basis for saying the two ends are functionally different and hence might produce different results one way versus the other.

Beyond that, if the darn thing has arrows on it, I point them downstream as instructed ie pointing from the source to pre-amp or pre-amp to amp. Just because there are arrows on the darn things, but for no concrete reason I could identify.

I've dabbled with a lot of wires over the years and am finicky about sound quality. But that's about the extent to which I worry about such things. Shame on me.

Some said, "define the signal." I define what it's not, how's that? It's not the electrons. AC is what, alternating current? Guess what? It's not the current either.