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

The reaction between two water molecules to produce hydronium ion and hydroxide ion is known as autoprotolysis of water. This is self ionization of water.
$2H_{2}O\to H_3{O}^{+}+O{H}^{-}$
This reaction indicates the amphoteric nature of water. It can act as an acid as well as a base. One water molecule donates electron whereas other water molecule accepts electron.