The reaction in which two water molecules react to give ions with proton transfer is called auto-protolysis of water or self ionization of water. A proton from one H2O molecule is transferred to another water molecule leaving behind OH– ion and forming a H3O+ ion.
H2O(l)+H2O(l) ⇌ H3O(aq)++OH(aq)−
Significance : Auto-protolysis proves that water is amphoteric in nature.