What is the role that CC do in the functioning of engine?

I had a doubt that CC means the volume of petrol/diesel outlet to engine..... , But will that makes the vehicle consumes more petrol/diesel if the CC is more?

Correct , larger the size of the engine, higher is the fuel consumption

Cc is nothing but cubic centimeters which is the total volume of the engine. So more the volume, more the air fuel mixture it absorbs. 

Where from does torque calculated in a car? And what is the proportionality between torque and performance?

Torque is measured using a dynamometer and the measure of an engine’s performance is torque