What do you understand by the term 'auto-protolysis' of water? What is its significance?

'Auto-protolysis' of water:

• When a self-ionization of water molecules takes place, producing hydronium $\left({\mathrm{H}}_3{\mathrm{O}}^{+}\right)$ and hydroxide $\left({\mathrm{OH}}^{-}\right)$ ions, the reaction is known as auto-protolysis of water.
• The chemical equation can be depicted as:

$2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)\to {\mathrm{H}}_3{\mathrm{O}}^{+}\left(\mathrm{aq}\right)+{\mathrm{OH}}^{-}\left(\mathrm{aq}\right)$

Significance of 'Auto-protolysis' of water:

• This reaction indicates that water is amphoteric in nature, which means water can serve as an acid as well as a base.