Fuel is needed to power up a car for different purposes.
Fuel is needed for performing a race in the GrandPrix. Depending on the selected race class (C, B, A or S) a amount of 2 up to 5 fuel is used.
Also fuel is needed in some of the Special Events like Pollos Banditos in Stage 2: Chicken Run.
And playing the Adventure fuel is needed to activate your car to smash the opposite Worker/Adventure Workers. Also, depending on which car you have, affects the amount of damage your car does.