The turbo increases the amount of air that is introduced to the engine. Mass airflow sensors see this increase in air and signal the fuel injectors to add proportionally more fuel.
This gives the net result of having effectively larger cylinders - the engine with the turbo can "process" the same amount of fuel per cycle as a larger engine with no turbo.
The weight of the turbo is very small relative to the weight of the engine, so this means there's an increase in the power-to-weight ratio of the engine.
This might be the answer you're after, but it's not clear because "efficiency" isn't well-defined when referring to automotive applications. There's "fuel economy" - how far you can go per unit of fuel, and there's "fuel efficiency" - how much mechanical power you get per unit of fuel.
The most fuel efficient point of an engine is generally wide-open throttle under maximum or near-maximum load (think accelerating from a stop). Fuel economy is dictated more by driving style, which includes minimizing acceleration rates, putting fuel economy at odds with fuel efficiency.
So, from that standpoint, if you were to drive a turbo-charged vehicle the same way you would drive the non-turbo counterpart, you would get the same accelerations at a lower throttle percentage. This would seem to imply better fuel economy at the cost of lower fuel efficiency.