So in acid solutions ions are present and electricity will flow through the mixtures. Perhaps the simplest kind of acid reaction is with a base. Bases are also electrolytes and most common bases are metal hydroxides like NaOH or KOH. Ammonia (NH3) is the only common base which is not a hydroxide. When acids react with bases, the same kind of "ion switch" happens as with a precipitation reaction. But instead of two ionic compounds forming, water is one of the products.
acid + base ® salt + water
HCl + NaOH ® NaCl + HOH
The formula for water is written oddly on purpose to show how this follows a familiar pattern. The term salt here means ionic compound. It is coincidence that we happen to call sodium chloride "salt". In this kind of reaction, we go from two electrolytes to one (water is not a good electrolyte, as your lab results from earlier experiments show).