It's nowhere near as deep as in a dedicated 4x game but it is there. HoMM games have a strategic, empire-building aspect. (Think HoMM4 actually let your hero fight? Regardless that's the exception in the series.)
You run into enemies on the overworld, go to a small hex based map, and fight out a tactical battle involving stacks of troops compressed into individual units, while your character sits in a magical skybox and fires off spells.
They have the same encounter and combat systems. Click to expand.Just to clear up the similarities and differences between the two: