MOSFET for revrerse voltage protection
So, what is the need of the zener diode in combination of the resistor
  in this circuit? How they are exactly working here?


The maximum gate source voltage for the FDN306P MOSFET is +/- 8 volts hence, on a 12 volt supply, if you didn't use a zener diode and the gate resistor you would be exceeding the limit specified in the data sheet.