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

Explanation

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:
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:
The reaction between fluorine and water can be represented as:
This is an example of a redox reaction as water is getting oxidized to oxygen, while fluorine is being reduced to fluoride ion.
The oxidation numbers of various species can be represented as:
Fluorine is reduced from zero to (-1) oxidation state. A decrease in oxidation state indicates the reduction of fluorine.
Water is oxidized from (-2) to zero oxidation state. An increase in oxidation state indicates oxidation of water.