Distillation is not, absolutely not, the same thing as boiling water, OK?
When you boil water, you raise the water to the boiling point (duh!) and drive some of the water molecules from the liquid phase (water) into the gas phase (steam). Whatever is left in the pot—the impurities—are still there. Only now they are dissolved in less water. As a result, the water is even more impure than before! (Although the bacteria and protozoans harmful to human health are often killed.) In distillation, the water is boiled and then the steam is captured. The steam is condensed, and it is this condensate which is the purified (distilled) water. Do you see the difference between this and just boiling water?