Water softened with salt has a high salt content which is why you shouldn't use it to water either your indoor or outdoor plants if possible. If you have high blood pressure, you probably shouldn't drink it either. An undersink mounted reverse osmosis system would be better for drinking water.
Water is softened by ion exchange - exchanging sodium ions for calcium and magnesium ions. Wikipedia has a good description.
Water softening - Wikipedia, the free encyclopedia
In reverse osmosis, water is forced through a membrane that filters out salt and other elements.