I wouldn't say that a turbocharger allows fuel to burn more completely, if that's what you meant. A turbocharger uses energy in the exhaust to spin a turbine, which is connected to an impeller, compressing air going into the engine. More air allows more fuel, and together you get a bigger bang in a smaller space - the engine behaves like it's larger than it is, burning more air and fuel then it would otherwise. A turbocharged car can still burn fuel inefficiently, and they often do run rich (injecting more fuel than will be burned) in order to avoid pre-ignition and to cool the cylinders.
A turbocharger may also be used to increase fuel efficiency without any attempt to increase power. It does this by recovering waste energy in the exhaust and feeding it back into the engine intake. By using this otherwise wasted energy to increase the mass of air, it becomes easier to ensure that all fuel is burned before being vented at the start of the exhaust stage. The increased temperature from the higher pressure gives a higher Carnot efficiency.
