The principal is the hydrogen helps burn the petrol/diesel more efficiently, wasting less of the petrol/diesels potential energy. The hydrogen itself requires more energy to produce than is generated by burning in the engine due to some of the energy being wasted as heat. IIRC studies on tractors found that around 40% of the potential energy of diesel is wasted straight out the exhuast and only around 12% of the energy in the fuel gest transmitted to the ground to move the vehicle forwards.
Studies using bio diesel and fossil diesl blends have found that the power output could increase slightly when a small % of bio fuel is added to diesel, though there was a paractical limit beyond which a higher % of bio diesel reduced the power output slightly.
Like a lot of engine tuning, just bolting bits on will not necisserily be beneficial. To get the best out of it will require more effort.