What happens when you mix vodka and water?

Mixing vodka and water gives you weak (diluted) vodka. Vodka is already a solution of ethanol (grain alcohol) in water, along with some flavoring molecules from the fermenting process, which uses grains or potatoes.

Vodka is from 80 proof (40% alcohol by volume) to 192 proof (96% alcohol). So this would be reduced proportionally by the addition of water. Water and alcohol are said to be "miscible", meaning they form a roughly homogeneous solution.