why does C1V1=C2V2 work

Other than it just being a "law," it's a rule of ratios.

Logically speaking, if you put 1 drop of food coloring into a glass of water, it will turn a certain hue. If you put this same 1 drop into a gallon of water, it will be less dark of a hue. You would need more drops of food coloring.

Hope that helped.