In a mixture, all the constituents are mixed randomly and not in a definite proportion.They are not Chemically bonded.In air also, all the gases are not chemically bonded and are not in a fixed ratio.They vary from place to place(although very minutely).All the gases in it can be separated.All the gases reatin their own properties. These all are the properties of mixture.

In a compound, The constituents are in a fixed proportion and chemically bonded.In water, you will always get Hydrogen and oxygen in a ratio of 1:8(By mass).We can't separate hydrogen and oxygen physically. Also,it does not retain the properties of its consttuents.Therefore, its a compound.

Hence, air is a mixture and water a compound.
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Air is a mixture because its composition is not fixed and the quantity of different gases in the air depend upon the place on the earth. 
  Air can be separated into its constituents such as oxygen, nitrogen etc. 
  Air shows the properties of all the gases present in it. 

Water is a compound because its constituents hydrogen and oxygen are always present in the same ratio as 2:1.
  Its properties are different from its constituent elements hydrogen and oxygen.   Also water has a fixed boiling point, which is different from that of both hydrogen and oxygen. 
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