It is not expected that typical users of the SlateWithManipulators prefab should need to either interact with or understand this script.
This script maintains scale based on the world-space relationship between a "local anchor" hierarchically parented to the transform on which this script resides and a "parent anchor" which is a hierarchical sibling. This logic is quite particular to that exact hierarchical configuration and is thus intended specifically for use within the SlateWithManipulators prefab.
The specific world-space relationship maintained depends on the scaling mode. The default is a two-dimensional scaling mode which attempts to maintain a constant world-space offset between the local and parent anchors. Explicitly, with the local anchor placed at the top left corner of the "slate" and the parent anchor set to the AnchorTopLeft of the SlateWithManipulators prefab, this script will rescale the local space such that the world-space relationship between the AnchorTopLeft (and the visual affordances attached to it) and the local anchor (which logically represents the top-left corner of the "slate" content) is kept constant. As this is a two-dimensional scaling mode, the Z scale or "depth" of the slate is scaled to maintain a constant world-space depth.
The spactial logic for the three-dimensional scaling mode is based on that of the two-dimensional scaling mode, but altered to maintain the original scale ratio of the content. This, as the name implies, is intended for manipulating object scale in three dimensions without squashing and stretching the object along the scaling axes. To this end, the script rescales the local space to find the largest aspect-correct scaling which can fit within the 2D rectangle described by the logic of the two-dimensional scaling mode. In other words, the three-dimensional scaling mode looks at where the slate content would have been placed by the two-dimensional scaling mode, then scales its 3D content to be as large as possible (without squashing) while still fitting within that "slate" space.