Strong acids tend to ionize completely. The ions are able to carry electricity across the solution creating an electric current
Distilled water conducts very poorly because there are very few ions in solution. Salt water conduct very well because salt ionizes completely in water.
Strong acid such as sulfuric acid are used in batteries because the acid ionizes so completely. The Hydrogen ions separate from the negative ion that they are attached to and are free to move electricity across the solution.
A solution can conduct electricity via the ions in the solution that carry a current between electrodes. Substances that dissociate into ions in aqueous solution and thus conduct electricity are called electrolytes.
Strong acids are called "strong" because they dissociate almost completely into component ions upon placing in water. This large amount of ions tells us that strong acids are good electrical conductors.