When an elctrolyte is dissolved in water, it splits up into ions.
For example, sodium chloride is the solid state exists as a collection of positively charged sodium ions and negatively charged chloride ions. These are held together by strong electrostatic forces of attraction in the solid state. Due to these strong attractive forces, the ions do not move freely and therefore do not conduct electricity in the solid state.
Ionisation process: When such a compound (NaCl) is dissolved in water, a high dielectric constant of water cuts down the forces of attraction between the ions. As a result, the ions get separated and dissolve in water.
The forces of attraction between oppositely charged ions are inversely proportional to the dielectric constant of the medium. The grreaer the dielectric constant, teh greater is the dissolving power of the solvent. The dielectric constant of water is 80 and therefore, these forces are reduced by a factor of 80 in aqueous solutions and ions become free to move.
(Topic: Ionic equilibrium)