Let's take common salt, #NaCl#, as an example. The solid species will not conduct electricity. Why not? Because the ions are bound (by electrostatic interactions) in a solid, infinite array, in which the individual ions that form the lattice are not free to move (and not free to carry a charge).
Raise the temperature enough (to #801# #@C#), and the sodium chloride melts, disrupting these strong ionic interactions, and now the ions are free to move, and can carry a current. We can get the same effect, if we dissolve the salt in water and chemically disrupt the bonds between the sodium and chloride ions. Now separated, and solvated by water molecules, these ions can transmit a current.