Question

Why does rain water conduct electricity and distilled water doesn't?

Answer 1

Electricity is conducted by those liquids which have ions present in them. Distilled water is pure and does not have negative / positive ions
therefore it can't conduct electricity.
Rain water is not pure and has ions in it.
so it can conduct electricity.

Answer 2

Rain water conduct electricity and distilled water does because distilled water is water in pure form and is neutral. Rain water is not pure water and dissociates into ions and so conducts electricity.  

EXPLANATION:

Electricity needs "ions" to move in electrolyte. Distilled water contains no ions and does not conduct electricity.

Rain water has dissolved salts and acids that dissociate easily into ions. Rain water is therefore able to conduct electricity.