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

Answer is: this is an example of an Arrhenius acid.

An Arrhenius acid is a substance that dissociates in water to form hydrogen ions or protons (H⁺). 

For example hydrochloric acid: HCl(aq) → H⁺(aq) + Cl⁻(aq).

An Arrhenius base is a substance that dissociates in water to form hydroxide ions (OH⁻). 
In this example lithium hydroxide is an Arrhenius base:

LiOH(aq) → Li⁺(aq) + OH⁻(aq).