Electrical current in water consists of the movement of charged ions in the water. So, for example, table salt contains two kinds of ions, positive sodium and negative chlorine. Those ions will move in response to an electric field if they are dissolved in water (they won't if they are locked up in a crystal, though). Pure water doesn't have many of these ions.

Hydrologists often test the "specific conductance" of a water sample to see how salty it is (how much dissolved solids it contains). What we're really measuring, though, is how that water is able to conduct an electrical current. When water contains dissolved solids, those free electrons can carry an electrical current. When water is very pure, electricity cannot be conducted through the water because there are no ions to carry the charge.