The chemistry
A material’s structure describes what its particles are and how they are arranged or connected. Its properties depend on those particles and the relevant conditions.
Electrical conduction needs charged particles that can move. Ionic solids contain charged ions, but those ions cannot move through the solid lattice. Molten ionic substances contain mobile ions. When sodium chloride dissolves, its lattice separates into hydrated Na⁺ and Cl⁻ ions, which can move and carry charge. Metals and graphite conduct using delocalised electrons. These electrons are not tied to one atom and can move through the structure.
Melting a simple molecular substance overcomes attractions between molecules. It does not normally break the covalent bonds inside every molecule. Giant covalent structures have a different bonding network.
Worked example
Solid sodium chloride does not conduct electricity: its ions are fixed in the lattice.
Molten sodium chloride conducts because its ions can move. The change in conductivity is explained by mobility, not by inventing free electrons in the melt.
Specification references
AQA 4.2; Pearson 1.21–1.42. These are broad topic references. Check the detailed statements in your specification.