By not having to start and stop like a conventional reverse cycle air conditioner the inverter models use much less electricity and also is much quieter as well.  To help explain this I will use an analogy.

Imagine you are driving your car.  You push the accelerator to the floor until you reach the speed limit and then you take your foot off completely.  When the speed drops below the speed limit you stomp on the accelerator again until you reach the speed limit and then take your foot off the accelerator completely.  Keep doing this as you try to maintain the car at the correct speed.  If you did this your fuel consumption would increase dramatically.  That is how conventional reverse cycle air conditioners work.  Inverter models work in a similar manner to the way you drive – as you reach the speed limit you ease back on the accelerator giving the car just enough revs to keep to the speed limit.