Auto protolysis of water is basically self ionisation of water. It is one of the chemical properties of water. Here, two same molecules react to give ions involving proton transfer.

This reaction also shows the amphoteric nature, which means water can act both as an acid as base.

(i) Water acting as an acid

Here, water acts as Bronsted acid and donates protons.

(ii) Water acting as a base

Here, water acts as Bronsted base and accepts protons.