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Basic Facts First:
  1. Pure dry salt does not conduct electricity.
  2. Salt dissolved in water does conduct electricity.
  3. If pure salt is heated to nearly a thousand degree Celsius, it becomes molten salt and does conduct electricity.
Basic Explanation:
Pure solid Salt is a crystal with positive and negative ions arranged in almost perfectly regular rows. Everybody is charged, but nobody can move so applying a voltage does not dislodge atoms from the crystal lattice sites. The atoms have electrons, but they too are tightly bound to the parent ion and won't move under any realistic voltage. There is a lot of charge, but it is not free to move, hence nonconducting.

Salt Solutions are a collection of charged ions moving more or less freely through water so they conduct electricity.

Molten Salt has the same ions as the solid crystalline salt, but they are no longer confined to a crystal structure. The positive and negative ions are free to move in the molten liquid and there is no water around. The molten form of salt has a lot of ions and they are free to move, so molten salts conduct electricity well.
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