Most filters are good at removing heavy metals and things like chlorine so the water may taste a lot better. They are not so good at removing other metals such as zinc, bacteria, viruses, fungus, mould, as these are elements that are not easily trapped by what in most is either activated carbon or small passages through a porous medium eg unglazed porcelain.
Reverse Osmosis (RO) or distillation are the cleanest outcomes but both require reasonably large amounts of energy to achieve results and RO also requires larger amounts of water (about 2 times more) than is saved/produced for consumption eg if you want 1 litre you need about 3 litres of uncleansed water.
