Turbo mode is a skill that everyone has when they first start out their character. (Default key 'R') You have entered turbo mode successfully when you see your Ki particles around you as if you were charging.
The 2 known things turbo mode affects are:
It seems to increase the speed at which the percentage of the power you are using goes up while pressing the charge button (default 'C').
It also increases your flying speed if you have unlocked the flying skill. (Note that transforming also does this.)