Question

"An acid is a substance that forms hydrogen ions when dissolved in water." this is an example of-

Answer 1

Hmm. This is very unspecific but it could either be indicating the pH of the solution or just saying it is an aqeous solution.

Answer 2

"An acid is a substance that forms hydrogen ions when dissolved in water." this is an example of Arrhenius theory .

Explanation:

Any substance that, after ionisation, dissolves in liquid and produce hydrogen ions called Arrhenius acid (HCl, HCN,etc). Whereas, a substance that dissolves in aqueous releases hydroxide ions called Arrhenius base (NAOH, KOH, etc).

Arrhenius theory elaborates why acids have same properties: The internal properties of acids are determined by the presence of $H^{+}$  ions formed by dissolving acids in aqueous. These also explain why acid neutralises bases and vice versa. Acids give an $H^{+}$ ion and the bases give an $O H^{-}$ ions.

Example:

                   $H C l \rightarrow H^{+}(a q)+C l^{-}(a q)$

Where, (aq) stands for aqueous which means in the presence of water that is, water acts as a solvent.