Convection microwave oven is a combination of a regular convection oven with a microwave, so you have both hot air and microwaves cooking your food. So the advantage is you get the quick interior heating of the microwaves combined with the surface browning from the hot air; convection just makes that hot air cooking faster and more even.
The microwave heats water and molecules in the food by using microwave radiation. It will heat food efficiently and quickly, but does not brown or bake like in a conventional oven.
The oven is used for heating from the bottom(baking, roasting) or from the top(boiling).The heat is from a single direction and not uniform.
Convection Oven has a fan that circulates heated air allowing operation at low temperature while cooking more quickly. It also results in more even bakes.
Convectional Microwave Oven is a combination of a microwave and a convection oven. Allows for even, quick cooking that is browned or baked.
So, at the bottom of the scale is a microwave and an oven. They each have different functions. Then there is a middle tier that would be a convection oven - an improvement over the oven. The top tier is the convection microwave oven that provides all the features: quick cooking, heating, baking, browning, and evenness.
HMC80252UC-MICROWAVE OVENS is the model that I am using.
I hope it is clear now.