What is this hole on the left wing of the Eurofighter Typhoon?
The Auxiliary Power Unit (APU) exhaust


(Source)

The item 72 is what you are looking for and it is labelled "APU exhaust". The black residue is soot from incompletely burned fuel.

The Eurofighter Typhoon can use its APU to start the main engine or to provide power when on the ground. From airvectors.net:


  The Eurofighter is also fitted with an auxiliary power unit (APU) for self-starting and ground power.


See also:


What is the APU actually used for?
Do fighter jets have an auxiliary power unit?