All in all, acid will decompose in water to give mobile ions, Such as H3O+ , SO4 2-, SO3 2-, NO3-............... In brief, acids are electrolytes. They conduct electricity well due to the presence of moblie ions. It conducts due to the movement of mobile ions.
Pure water merely has mobile ions. Since it is a molecule, the electronegativity of oxygen and hydrogen is not differ to much, the probability of water molecules pull off an ion out from an other water molecule is low. Hence, water is not a electrolyte.
Adding small amount of dangerous sulphuric acid make it perfect.
By the way, YT, how to extract potassium from its own ore?