A dentist score between 0 and 4 indicates zero is the best you can get, meaning your gums are in excellent condition, and four indicate gum disease. The numbers your dentist hears calling for are the depths of the pockets around your teeth in millimeters. The background is a little more confusing. While the upper part numbers the right side first, it is the opposite for the lower part.
The lower left is quadrant three and the lower right is quadrant four. From the dentist's perspective, they look up and down inside the mouth. It is easier to list quadrants so that the section under quadrant two is quadrant three. Usually, 1 — 3 mm is healthy, 4 is a warning, and anything above 5 is a call to action to prevent disease.
When engraving a 5 or 6 mm bag, deep cleaning may be recommended. Rarely, when the numbers are higher, gum surgery is performed. The stitches are later removed and healing is evaluated. If you hear numbers of 0 or 1, you're doing quite well.
There is great information about the British Society of Periodontology to help you keep your gums in good shape.