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Sodium chloride is an ionic compound and thus it has giant ionic structure. Solid sodium chloride lattice consists of a huge number of sodium and chloride ions which are held together by strong electrostatic forces. Therefore, it needs a lot of energy to break the lattice of sodium chloride, and thus sodium chloride has a high melting point.
In solid state, the sodium and chloride ions are well arranged and are not mobile. Therefore, there is no mobile ions (or delocalized electrons) to conduct electricity, and thus solid sodium chloride cannot conduct electricity. When sodium chloride is melted in a molten liquid, it can conduct electricity because there are mobile ions to conduct electricity.