If you drink truly pure H2O (but we can just call that water, you know), you would get sick because you would trigger reverse osmosis in your stomach and intestines. I don't know if you could drink enough to die from it.
The simple theory here is that nature abhors imbalance. When you eat, the cells in your digestive system absorb nutrients due to the "chemical potential" difference in which the mineral content of the stomach is highly concentrated with respect to the naturally lower mineral content of your cells. But if you drank totally purified water, like double- or triple-distilled water, the mineral content of your cells would be far higher than that of the water you just drank and the minerals of your cells would move in the other direction, flooding the stomach with "leached" nutrients and draining those nutrients from the cells. It would act very much like a chemical burn. Even though the cells have walls, those walls are semi-permeable... meaning that things can pass through them slowly. Things like minerals and nutrients.