Just to add to what Nick said...
The main benefit of water injection is to cool the air/fuel charge entering the engine, whether piston or turbine. Water injection is normally only used where air is compressed before the air/fuel charge is burned, as in a piston engine with a turbo or supercharger, or a gas turbine.
By cooling the air charge, destructive detonation (caused by high fuel temp) can be delayed in the boosted piston engine, and a destructive TOT can be lowered in the turbine engine. The main benefit for both engine types, is that a larger air/fuel charge can be feed into the engine and burned without causing damage, while the water injected cooling is taking place. The burning of this larger air/fuel charge (made possible by the water injection cooling) is where the extra power comes from.