What is the function of the hole at the rear of the airplane?
This one? It's the APU(auxiliary power unit)'s exhaust.

An auxiliary power unit (APU) is a device on a vehicle that provides energy for functions other than propulsion. 


  The primary purpose of an aircraft APU is to provide power to start
  the main engines. Turbine engines must be accelerated to a high
  rotational speed to provide sufficient air compression for
  self-sustaining operation. Smaller jet engines are usually started by
  an electric motor, while larger engines are usually started by an air
  turbine motor. Before the engines are to be turned, the APU is
  started, generally by a battery or hydraulic accumulator. Once the APU
  is running, it provides power (electric, pneumatic, or hydraulic,
  depending on the design) to start the aircraft's main engines.
  
  https://en.wikipedia.org/wiki/Auxiliary_power_unit