When we touch the switch with wet hands, the electricity that is already flowing passes through the water because it has a few ions which are enought to flow current. But when you talk about electrolysis, we have to make electricity and we need more anion and cation. Pure water is insulator, so we add acid
Because water is insulator or we can say that it has high dielectric constant (=permittivity÷permittivity of free space) so it do not conduct electricity , it has no ions (no doubt it has ions but are counted as negligible) to move ; in order to make it ionic (presence of ions) acid is added because according to Arrhenius theory when an acid is dissolved in water,it releases H+ or hydronium ions(H+3O)
So in this way these ions helps to conduct electricity