The Chloride is an ion because it has gained electrons.
In order for it to become pure chlorine it has to lose those electrons, hence the 2Cl- + 2e- --> Cl2
The chlorine is a negative ion, that's called an anion in chemistry. The anode is the electrode which is positive.
Therefore, the anions go to the anode and vice versa for the Hydrogen.
But because it's an aqueous solution, it's different than molten electrolysis.
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