Why is there oxidation in the anode?
We define anode to be the electrode where oxidation takes place.

Oxidation signifies loss of electrons and Reduction signifies gain of electrons.

For example, in this electrochemical cell,



Copper has more reduction potential than Zinc. So it will be easy for copper to reduce (or gain electrons) and if copper is reducing (or gaining electrons) then there must a source of these electrons. These electrons are supplied by Zinc (which gets oxidized). 

At anode, $Zinc(s)$ in losing electrons and converting into $Zn^{+2}(aq)$ ions and at cathode, $Cu^{+2}(aq)$ ions are gaining these electrons lost by $Zinc(s)$ and converting into $Cu(s)$.

These reactions occur because they are spontaneous $(\Delta G =-ve)$. Spontaeous reactions occur in nature by themselves without any external driving force. A system aims for least energy $(\Delta H = -ve)$ and maximum entropy $(\Delta S = +ve)$ and its the combination of both these factors that result in spontaneous processes. $(\Delta G = \Delta H - T\Delta S)$.