Forgive me but what on earth does meth do?!
Cools the charge.
The turbo compresses the air, which heats it up. Intercoolers are in place to help dissipate this extra heat, but Water-Methanol Injection sprays a mist of fluid into the air inlet which cools it even further as the liquid evaporates - like spraying a fine mist of water on to your face! It's the evaporation that sucks a load of latent heat of of the air.
The cooler the air charge, the denser it is, the denser it is, the greater the mass of air you get in the cylinder, and the more air mass you get in the cylinder, the more fuel you can chuck in there to burn!
Also has the effect of cooling the exhaust outlet temperature (good for managing exhaust header temps, engine bay heat soak etc.).
The Methanol is in the mix to add a bit of calorific value to the WMI charge.. Straight water could hinder combustion a bit as the water can soak too much heat once in the cylinder (combustion timing gets retarded), straight methanol whilst it has a cooling effect on the charge will usually result in higher exhaust temperatures as pure alcohols burn hot!
Somewhere between a 30:70 (methanol:water, pretty much winter strength screen wash) and a 50:50 mix is usually about right.
There are also knock on benefits I've seen claimed - can help keep things from gumming/coking up as the head is essentially getting a light steam clean every second rotation, presence of water in the cylinder can help maintain a longer power stroke by providing more mass to expand under the adiabatic heating, all sorts of things...
Downsides are it's another system that needs maintenance, and another fluid level that needs checking and topping up. Water will get everywhere in the head, so for cast iron blocks rust/corrosion can be an issue (perhaps not so much with out Aluminium blocks), and the dangers of relying on WMI to push the engine tune are that you can seriously overheat things if you run out of water/meth whilst driving.
Not a tweak for everyone, but an interesting one to follow definitely!