Water is the most important solvent that we deal with. Water molecules are very polar. As such, they form solutions that are really unusual in nature. Ionic solids, such as NaCl, are made up of ions -- electrically charged species -- interspersed with one another in extremely regular arrays or lattices. In these solids, the ions cannot move, so ionic solids do not conduct electricity. Heating an ionic solid until it melts gives a liquid that does conduct electricity.
Water solutions (aqueous solutions, from the Latin aqua for water) of ionic salts also conduct electricity. The solution formation process leads to solvent-separated ions that, because they are mobile, do conduct.
Some solutes that are not ionic also form solvent separated ions in solution. HCl, a gas that is very soluble in water, dissociates or breaks up almost completely in water to form solvent separated hydrogen ions (H+) and chloride ions (Cl-).
Solutes that dissociate completely into solvent separated ions in water solution are called strong electrolytes. Many substances dissociate only partly into solvent separated ions. These substances are called weak electrolytes. Acetic acid (vinegar, CH3COOH) and ammonia (NH3) are examples of a weak electrolytes.
Some materials dissociate so little that their solutions don't conduct electricity any better than does pure water. These solutes are called nonelectrolytes. Ethanol (C2H5OH) and table sugar (sucrose, C12H22O11) are examples of nonelectrolytes.
Water itself breaks up just a bit to give ions:
H2O H+ + OH-
Water is thought of as a nonelectrolyte in spite of this small degree of dissociation.
The notion of electrolytes is really important. For example, reactions in solution usually are described in terms of reaction ions rather than dissolved solutes. So, chemists write net ionic reactions [local].