What do you understand by the term ’auto-protolysis’ of water?

Auto-protolysis (self-ionization) of water is a chemical reaction in which two water molecules react to produce a hydroxide ion ( $\mathrm{OH}^{-}$) and a hydronium ion $\left(\mathrm{H}_{3} \mathrm{O}^{+}\right)$.

The reaction involved can be represented as:

Auto-protolysis of water indicates its amphoteric nature i.e., its ability to act as an acid as well as a base.

The acid-base reaction can be written as: