When the sodium chloride is dissolved in water, the ions forming the ionic solid separate out. This means that there are actually 4 ions present in the solution: H+, OH-, Na+ and Cl-.
This electrolysis can be demonstrated using a U-Tube, although this is not the industrial set up

Anode:
- The indicator turns red initially, and is then bleached to colourless.
- This indicates the presence of chlorine.
- The negative ions are attracted to the positive electrode.
- The chloride ions are discharged (giving chlorine) in preference to the hydroxide ions.
- These are left behind in solution.

Cathode:
- The product at the negative electrode is hydrogen.
- At the negative electrode the indicator turns purple.
- At the negative electrode, the hydrogen ions are discharged (producing hydrogen gas) in preference to the sodium ions.
- These are also left behind in solution.
- Thus sodium hydroxide solution remains. This is the cause of the purple colour of the indicator at the negative electrode.

Some of the water will ionise, that is, turn to hydrogen (H+) and hydroxide (OH-) ions.

The remainder of the solution stays green.

In time, the green colour of the indicator in the middle would change too, as the ions diffuse through the resulting solution.