Water does actually make a more efficient burn - somehow. I'm not a chemist so don't really know the full story.
Naturally, efficiency = less petrol needed. There is a limit to which it works, though although the actual mix can be quite surprisingly high.
Chucking anything inert into a petrol engine, when it's partly loaded, will increase efficiency because the engine doesn't have to be throttled back as much, and throttling the engine increases the losses. It's almost like reducing the capacity of the engine because part of the cylinder volume is effectively removed from the equation. This is the principle behind exhaust gas recirculation too.
Water is even better because it absorbs heat from the combustion process and expands as it vapourises. This expansion adds to the pressure forcing the piston down and allows the engine to recover more of the energy of combustion into useful power.
It has downsides because it reduces the temperature of combustion, and this affects emissions IIRC.
It is also useful in turbocharged engines running a lot of boost as it reduces charge and combustion temperatures. It does reduce the ultimate power output for a given boost but can be used when the intercooler is struggling to stop the engine lunching itself.
Kevin