The manual post-hole auger relies on the twisting motion of the angled thread to cut into the ground and pull the tool downwards.
The spiral shape means that the thread travels along the path that the cutting edge is creating through the soil, without disturbing the soil too much.
This moves the threads to below the soil that needs to be removed to make a hole. When the auger is pulled out of the ground the soil is pulled out with it because it is caught between or above the thread.
This process creates a very neat hole in comparison to using a spade which needs a much larger space to get underneath the soil to lift it out of the ground.