Distilled water is pure water and lacks any ionic species. It has pH 7 i.e. neutral. It also doesn't contain any dissolved salts or impurities. It is devoid of free electrons due to which movements of ions don't take place. Therefore, it does not conduct electricity. Whereas, Tap water being a not entirely pure form of water contains many ionic species such as acids and dissolved salts, and impurities that help in the movements of ions therefore it conducts electricity.