Question

Why does distilled water not conduct electricity,whereas rain water does???

Answer 1

Because these are charged when they move through water , electricity flows through liquid. In distilled water, there are no impurities , there are no ions, there are only neutral ( no charge) water molecules and these neutral molecules don't have charge, so distilled water does not conduct electricity.

Answer 2

Distilled water as such does not contain any mobile electrons which are necessary to conduct electricity so by adding impurities we make it a conductor. The same applies to rain water. It already contains a bunch of impurities which make it a better conductor than distilled water.