The girdle of your diamond runs around the outer edge between the upper crown facets and the lower pavilion facets.
It is the thin outer edge, separating the upper part of the diamond from the lower section. The polished, faceted or bruited (matt) girdle includes the number applied microscopically.
SGL laser inscription gives you the confidence of purchasing a diamond. Retailers must use this as a further selling point since not all laboratories laser mark diamonds in this way.
SGL records the stone under this number in their online archive. The inscription is almost invisible to the naked eye and can be seen under 10x magnification.