Like any growing thing, plants need nutrients to survive and grow. While plants also need plenty of oxygen to enable them to absorb nutrients, air alone can't actually provide them.
In aeroponics system, concentrated nutrients are diluted in water and misted onto the roots of plants. In high pressure and fogponics systems, the mist droplets are so small and oxygen so plentiful that roots are able to absorb and utilize the nutrients immediately. This means that aeroponics systems use lower concentrations of nutrient solution and there's virtually no waste.