Why doesn’t distilled water conduct electricity?

Distilled water does — but very little compared to piped, well or salt water. The reason is that the way a liquid conducts electricity is by the positively or negatively charged ions that are actually moving from one of the electrodes to the other, carrying charge (electricity) with them. Salt water has salt in it, NaCl, which readily ionizes or dissociates to ions of Na+ and Clthat can float through the water carrying charge and thus conduct electricity. Distilled water is water that was boiled to steam and recondensed to water. So distilled water is relatively pure H2O. Water can ionize to H+ and OH- like salt does, but it ionizes to a far lesser degree and is very resistant to conducting electricity.