Directional cables - what does that really mean?

We can measure the precise speed of the electrons. That much is certain.

1. Cables with shield connected at one end.
2. Conductor Extrusion effects.
3. Cable architectures

No. 1 can affect noise, could be sonically discernable, and so should be followed,
No. 2 can be discerned visually by microscopy but I have never heard of this being reliably identified in a listening test and IMO falls into the same category as directional fuses, jackalopes, and other urban myths, so...if you want to believe then believe, and
No. 3 is pretty simple...if there are arrows on your cables, point them in the downstream direction, e.g., from the source toward the speakers.
for the believers...

@WillieWonka - Thank you for the summary, makes sense for practical use. I continue being suspicious about the arrows, but I understand and agree with your explanation: some of the reasons are legit. Thanks.

@Jea48 - Yes, the audio signal is brought upon by the electrons doing a little alternating dance back and forth, and pushing/pulling on their neighbors to dance with them, and their neighbors pushing their next-next neighbors etc... If they would be marching together towards the end of the cable without coming back to about their original location - that uniform movement would be a DC signal that carries no audio info by itself.

Interconnects are obviously better sounding in one direction than the other. No bout a doubt it. So are fuses. Even big standard non audiophile grade fuses. No offense intended to anyone.