Question

Why can sodium chloride conduct electricity?

Answer 1

Because it's an electrolyte.

Explanation:

Electrolytes in water solvate into their respective ions, in this case: `Na^+` and `Cl^-`.

Answer 2

Sodium chloride as a solid is not a good conductor of electricity until it has been dissolved in water or has been melted to become molten `NaCl`.

Explanation:

Solid `NaCl` maintains a crystalline structure that does not have free electrons as in the lattice structure of metals. But when dissolved in water, the crystalline structure is broken down and the salt molecules become ions. This also occurs in molten `NaCl`.

The dipoles in the water separate the `NaCl` into `Na^+` cations and `Cl^-`anions during solvation so the solution can conduct electricity.

But before you run out and replace your house wiring with tubes of sea-water, you should know that the chemical reaction producing the conduction of electricity is limited by the concentration and availability of `NaCl` and water. (And gas venting.) So unlike electron movement in wires, the chemical process does not go on indefinitely.

There is more information here under electrochemistry:
https://en.wikipedia.org/wiki/Electrolyte