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

Auto-protolysis (self-ionization) of water is a chemical reaction in which two water molecules react to produce a hydroxide ion $(OH^{-})$ and a hydronium ion $(H_{3}O^{+})$. The reaction involved can be represented as:
$H_{2}O_{(l)} + H_{2}O_{(l)} \leftrightarrow H_{3}O_{(aq)}^{+} + OH_{(aq)}^{-}$
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:
$(H_{2}O_{(l)})_{\text{acid}} + (H_{2}O_{(l)})_{\text{base}} \leftrightarrow (H_{3}O_{(aq)}^{+})_{\text{conjugate acid}} + (OH_{(aq)}^{-})_{\text{conjugate base}}$