Answer
The Geographic Transformation parameter is used to set a default transformation for a geoprocessing tool that would not normally have this option available.
For example, if data defined as WGS 1984 is being imported into a NAD 83 feature dataset using the Feature Class to Feature Class tool, the option to select a transformation does not exist. Therefore, ArcMap uses the Geographic Transformation parameter in the environment settings instead.
However, if a feature class in WGS 1984 is being reprojected to NAD 1983 using the Project tool, it uses the selected transformation as set by the Transformation pull-down menu and overrides the environment settings.