Do the maths - W = V x I
In a linear circuit you might have 5V across the FET and 10A through it - so 50W of heat in the FET (10 x 5).
In PWM the FET (or transistor) is either fully ON or fully OFF - so assuming a 10V supply:
FET ON - current = 10A, voltage = 0V (or close to it), W = 0 x 10 (so zero watts).
FET OFF - current = 0, voltage = 10, W = 10 x 0 (so zero watts).
Add OFF and ON together 0 + 0 = 0, so zero watts total.
In practice the voltage drop across the FET will be slightly above zero, but still very low, and the FET will be briefly in linear mode as it switch between ON and OFF, and OFF and ON - which is why it's important to switch as fast as possible.
This is why PWM and switch-mode have taken over the electronics world.