Water Injection, why does it help boosted engines?

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Water injection actually does 2 things to reduce knock:  The heat of vaporization cools the incoming charge and the net reduction in inducted temp has a direct knock resistance benefit.  The second (separate) benefit is the benefit of humidity on knock resistance.  Regardless of temperature, higher humidity reduces knock tendency (like raising Octane).  The humidity benefit is a function of the how it changes the ratio of specific heats (think of it as a chemical property) of the mixture, and also changes some of the complex chemistry of combustion.  And yes, the ambient humidity does effect knock tendency.  The worst weather for knock is hot and dry.

Methanol mixed with water also has the chemical effect of increasing Octane chemically, since Methanol has a very high Octane number.

For most effective water injection benefit, inject the water as close to the intake valves as possible, so more of the heat of vaporization goes into the cylinder and less into the intake system.  The most effective water injection is directly in the cylinder (like where the GDI fuel injectors are).  You can find several SAE papers published on this.  

Finally, realize that (except for direct water injection) the water displaces some air and so the turbocharger has to work harder to force the same amount of air in the cylinder.  This is why water injection can actually reduce power at low revs when the turbo is already working as hard as it can (wastegate closed).

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