Why is water known as an acid as well as base?

Because water molecules can both split off and accept a proton H+ :

• H2O + H+ ---> H3O+ (hydroxonium ion)
• H2O ---> H+ + OH- (hydroxide ion)

This is called the 'Water equilibrium of internal protolysis:

• 2H2O <==> OH- + H3O+

  pKw = 14 or Kw = [H3O+]*[OH-] = 10^(-14)