Acids are species with pH less than 7, while bases those with pH greater than 7. Depending on the definition used - Arrhenius, Bronsted-Lowry, or Lewis - acids can be described as proton donors, or electron acceptors while bases as proton acceptors or electron donors. Using Arrhenius' definition, acids are those that produce the hydrogen ion when dissolved in water (`H^+` ) while bases produce the hydroxide ion (`OH^-` ).
These ions, when in water, act as charge carriers and can hence conduct electricity. Stronger acids dissociate completely and produce more of the ions. For instance, hydrochloric acid, a strong acid, would dissociate more, and hence, conduct electricity more strongly, while acetic acid is a weak acid, and would conduct more weakly.
The general term for substances that conduct electricity when dissolved in water is electrolytes. Acids and bases are electrolytes due to the production of hydrogen ions and hydroxide ions.