First of all, good quality drinking water should be pure and should not have any significant level of toxic biological or chemical contaminants. A good level of purification can be achieved by reverse-osmosis (RO) filter systems, or by distillation of tap water.
Further, good drinking water should have a significant level of healthy minerals, particularly calcium and magnesium. Unfortunately, it is not possible to be sure about the quality of drinking water simply by tasting it, looking at it, or even by filtering it. Some testing and/or information gathering is typically required. Please see response to next FAQ question for more info.
It is also important to note that mineral cartridges or remineralizing filter systems typically do not provide proper levels of balanced minerals. Always ask the filter supplier for details and written specifications! For example, ask exactly what minerals are being added into the water, and at what levels? Further, is the cartridge certified by any reputable agency such as NSF?