Hi,
The geometric error defines the error, in meters, when a tile is rendered, but its children are not. So, for example, this is zero for leaf tiles because their contents represent the original dataset at full resolution.
For non-leaf tiles, the geometric error depends on the type of data (e.g., buildings, point clouds, terrain, etc.) and how significantly it was decimated (e.g., buildings that were removed, points that were removed, vertices that were merged creating a lower level of detail). For a concrete example for terrain, see the Hausdorff distance in Slide 17 of
Rendering the Whole Wide World on the World Wide Web.
Patrick