pulse width modulation versus amplification
The power dissipated in the transistor is P=IV where I is the current through the transistor and V is the voltage across the transistor. 

When the transistor is fully on V is small and therefore P is small.

When the transistor is fully off I is very small and therefore P is very small

When the transistor is partially on both V and I are significant and so P is much larger.

Note though that to make a PWM based system efficient you need the right kind of filter, you don't want resistors in your filter because they waste power, so you would normally use a LC filter. You also need to make sure that when the transistor is off the inductor has a path to discharge, either by a diode or a second transistor.