Distilled water is literally water that has been boiled, evaporated and condensed - leaving all chemicals, toxins and waste behind and creating pure, clean water. Distillation will remove bacteria, viruses, cysts, heavy metals, radionuclides, organics, inorganics, and particulates.
Distillation is literally the method seen in nature, whereby: the sun heats the water on the earth's surface, the water is turned into a vapour (evaporation) and rises, leaving contaminants behind, to form clouds. As the upper atmosphere drops in temperature the vapours cool and convert back to water to form water droplets. Then once the droplets fall as rain (precipitation) the cycle starts over again.
This is exactly the same process in a water distiller - the tap water is heated to boiling point so the impurities are separated from the water, and the water then becomes steam. This is then condensed back into pure liquid form. The impurities remain as residue and are removed leaving 100% pure, pH balanced water.