Question

Why does distilled water not contain electricity?

Answer 1

Distilled water is boiled into vapour and condensed back into liquid in a separate container. Impurities in the original water that do not boil below or near the boiling point of water remain in the original container. Thus, distilled water is one type of purified water.

Complete answer:
Distilled water is a pure form of water which does not contain any solute in it therefore it cannot conduct electricity because it does not contain ions while rain water contains dissolved salts and acids which dissociates in ions and conducts electricity.
A liquid conducts electricity by positively and negatively charged ions that are actually moving from one of the electrodes to the other, carrying charge or electricity with them. Salt water has salt in it, $NaCl$ which readily ionizes or dissociates to ions of $N{a^ + }$ and $C{l^ - }$ that can float through the water carrying charge and thus conduct electricity. Distilled water is water that was boiled to steam and re-condensed to water. So distilled water is relatively pure ${H_2}O$. Water can ionize to ${H^ + }$ and $O{H^ - }$ like salt does, but it ionizes to a far lesser degree and is very resistant to conducting electricity.

Note: Dissolve a pinch of common salt in distilled water. When salt is dissolved in distilled water it becomes a salt solution. By passing a current through it, we observe the magnetic needle of the compass show deflection. Thus, distilled water becomes a good conductor of electricity on dissolving a little of salt in it