A good example is table salt
Table salt at room temperature is a lattice structure-- meaning its ions are SUPER close to each other and hence can't flow.
If you look at electrical insulators, it simply means they can't carry charge-- because there's no flow of charge.
If you dissolve table salt or melt it, it becomes Dissociated meaning NaCl becomes Na^+ and Cl^-
So now they are separated, and they are ions (charged particles)-- because they are separated they can flow, and because they are charged, they carry a charge. Hence, a flowing charge when they are melted (at super high temperatures) or dissolved (yes, even at room temperatures)