In piston engines, water (or water/alcohol) injection cools the intake charge and that helps prevent detonation at high compression rations/boost pressures. Not only does detonation kill performance, it can rapidly kill the engine (I used to have a nice collection of pistons from my racing showing just how much damage even a few seconds of detonation can do to piston - including pistons with holes through the crown).
Turbine engines also use water injection to cool the intake air to allow more fuel to be added and burned without over temping and melting the turbine blades - producing more power. Yes, there is a small delta in thrust due to the added mass of the water to the exhaust stream, but that's secondary and small. The big gain is that you can burn more fuel which means more power (thrust).