My students may not fully appreciate the significance of seeing the conductivity rise. How can I deepen their understanding?

You might ask them at the start to predict the conductivities of pure water, glacial ethanoic acid before demonstrating these. Then speculate about what might happen when the water is added. This will help them to focus on what is happening. Then discuss why they have seen the enormous effect on conductivity demonstrated.

Why is alternating current, AC, used rather than direct current, DC, in this demonstration?

AC is used to avoid electrolysis from taking place to any significant extent (at least, any extent that would interfere with experiment).

I gave this demo a brief trial myself but I didn't see anything happening. What might be the problem?

The issue is likely to be adjustment of the scale on the ammeter. Try to put it on the most sensitive AC amps scale. When you have added some water you should see a reading at least, and you should certainly see the condutivity reading rise when you are pouring in a significant amount of water.

Why are the electrodes copper foil strips?

Copper foil electrodes provide a convenient method of enabling the electrodes to fit the entire depth of the beaker and are secured very simply by folding at the top. The diluting effect of water is not important since the electrodes run the full height of the beaker (when more water is added, more surface area of the electrode is available – current depends on the number of ions present).