How it Works
The most basic explanation is that a current is drawn from the electrical system and runs through a set of electrodes immersed in a water and electrolyte solution, causing electrolysis to occur. The oxygen and hydrogen created by electrolysis is fed into the engine via the air intake. If you want to understand in greater detail why the qualities of hydrogen result in a greater combustion efficiency when mixed with other fuels, take a look at these articles from scientific journals that show the results of laboratory tests.
Research
Combustion Science and Technology
Society of Automotive Engineers