The main advantage of white fillings (composite filling) is their aesthetic appeal: they are matched with the colour of your teeth so are natural looking. White fillings are mercury free, needs less tooth preparation (drilling), making composite a less destructive restoration.
White fillings are bonded (adhesive) to the tooth structure and this allows the dentist to build-up chipped or fractured front teeth or even build-up badly broken down teeth. The main disadvantage is their life expectancy. White fillings have always been considered less long lasting than silver amalgam fillings but there are now new materials available with properties comparable to silver amalgam, and these are very successful.