To say it another way: Why does H2O dissociate easily into H+ and OH- when NaCl and electricity are added but not when only electricity is added?
Water dissociates into OH-
(almost) exactly the same way no matter whether other ions are present, or not. In both cases concentrations of OH-
are defined by the water ion product - and are very, very low, in the 10-7
M range (that is assuming there are no acids/bases added). Such a small amount of ions means very high resistivity (if memory doesn't play tricks on me ultra pure water has a specific resistivity around 18.2MΩ/com).
How does the presence of ions allow current to flow and cause this dissociation to happen? I get that ions are free to move in solution and move towards their respective anode and cathode.
What is the electric current? How is it defined?
I don't understand why water, which is not ionized, participates in the reaction at all.
Why should it not? Nothing unusual in neutral molecules being reduced/oxidized. While reduction and oxidation always mean charge of transfer, it doesn't mean product or reactant have to be charged.