The signal - throughout it's entire path - is a two-way, push-pull, alternating current (AC) signal, so your speaker cones go in and out at the frequencies of the music being played and vibrate the air molecules to make sound.
In other words, the signal is travelling in both 'directions' (on both conductors) many thousand's of times per second. The net distance travelled is (approximately) zero and the signal will spend 50 percent of the time 'pushing' and 50 percent of the time 'pulling'.
If the signal were to act like a stream or river (direct current or DC) - going in only one direction from source to speaker like some people imagine - then your speaker cones would remain static (either pushed out or pulled in permanently without moving) and the driver's coils would heat up and melt because the electrical energy would not be converted to movement. Just heat.
This is why the arrows are meaningless and 'cable directionality' nonsense.