Electrical conductors contain charges that are free-moving. Acids are proton (H+), or hydronium ion (H3O+), donors. Protons are charged. Thus, acids are able to conduct electricity.
When an acid is dissolved in water, it undergoes an equilibrium reaction. This reaction can be represented as follows:
HA + H2O ↔ H3O+ + A-
The amount of ionization of an acid has to do with the stability of an acidic compound and its likelihood to dissociate. The amount of dissociation of protons within an acid has to do with the polarity of the covalent bond that connects hydrogen to another atom (the H-A bond). Polarity has to do with the electronegativity differences between the atoms that share a covalent bond. The more electronegative the conjugate base (A-) within an acid, the more polar the H-A bond, the more likely the hydrogen is to dissociate, and the stronger the acid.
Stronger acids dissociate more easily. Therefore, stronger acids produce more ions. Thus, stronger acids are better conductors of electricity than are weak acids.