Water is probably the most important and frequently overlooked contribution to our overall diets, and finding the safest and healthiest source of drinking water has only gotten more complicated through the years. Bottled water, tap water, spring water, osmotic water, filtered water, and distilled water all have their proponents.
Distilled water in particular is often preferred for its greater clarity. The distillation process (boiling water and collecting the condensed evaporative steam) kills off pathogens and removes virtually all contaminants from the source water. However, this removes the virtuous components of a natural water source at the same time, including essential minerals.
NB: Fluoride is not removed in the distillation process, and in some cases aluminum ions can be introduced to the water through distillation.
Overall, distilled water can be a good way to otherwise avoid tainted water sources, but most drinking water sources are generally safe. Some specific cases definitely require distilled water or similar, but for most people it is probably unnecessary. As to the lack of mineral content, most of our dietary mineral intake is food-based, and so our water sources should make minimal differences one way or the other.