It is found that even purest form of iron can conduct electricity in small extent. So for the conduction of electricity, there must be ions in water. The formation of ion in pure water can be explained by the phenomenon called auto ionization of water.
During the ionization of water, some of the molecules act as Bronsted acid and some other acts as Bronsted base, so there is acid base reaction among the water molecule which results in the formation of hydronium H3O+ and Hydroxide OH– ions. These ions are responsible to conduct the electricity. This interaction among the water molecule to form hydronium ion and hydroxide ion is called auto ionization of water.