When electrolyzing Aqueous $NaCl$, several species compete at the electrodes:

• At Cathode (Reduction): Both $N{a}^{+}$ ions and $H_{2}O$ molecules are present.

1. $N{a}^{+}+e^{-}\to Na(s)$ ($E^{\circ }=-2.71\text{ V}$)
2. $2H_{2}O+2e^{-}\to H_2(g)+2O{H}^{-}$ ($E^{\circ }=-0.83\text{ V}$)

• Selection: The reaction with the higher (less negative) reduction potential occurs more easily. Since $-0.83>-2.71$, Hydrogen gas is evolved at the cathode rather than sodium metal deposition.