${\mathrm{H}}_2\mathrm{O}+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons {\mathrm{H}}_3{\mathrm{O}}^{+}+{\mathrm{OH}}^{-}$ In this reaction water acts as
I ) Bronsted Acid 
II) Bronsted Base
III) Amphoteric oxide

Water has the ability to act as an acid as well as a base i.e., it behaves as an amphoteric substance.

This is due to Auto-protolysis of water.

${\mathrm{H}}_2\mathrm{O}+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons {\mathrm{H}}_3{\mathrm{O}}^{+}+{\mathrm{OH}}^{-}$