Via holes are drilled on the layers of a multilayer PCB to establish an electrical connection between the layers. The Annular Ring is the area (area of the copper pad) that surrounds the drilled and finished via. These annular rings establish a good connection between the vias and the copper trace.
This dimension is recommended because the plating on the holes has to be done properly. This is the minimum required dimension. However, it is better if it is more than a 0.15 mm(6mil) gap for via holes.
An Annular Ring Width = (diameter of the pad - diameter of the hole) / 2
The quality of the plating on the holes will be better if the via holes dimension is 0.4 mm.
The image below shows the exact dimension of the via hole and the annular ring,
