In FME versions previous to FME 2009, Enhanced Geometry was referred to as Rich Geometry. It has been renamed to more accurately reflect its function in FME.
It is important to understand that, for the most part, the geometry model will be transparent to users. You will not have to change the way you use FME or set up a workspace. The only visible difference should be improved output (if there was room for improvement).
Workspace Navigator > Advanced Settings > Geometry Handling. Valid values are Enhanced and Classic, and the default is Classic.
The addition of enhanced geometry model support allows lines and polygons containing arcs to be maintained, rather than stroked or the geometry split up into multiple segments. It also provides the ability to truly hold measures.
A global directive (in the form of an Advanced setting in Workbench) sets the usage of enhanced geometry in readers/writers and factories/functions/transformers that were created using "classic" geometry. All new readers/writers and factories/functions/transformers use enhanced geometry and are not affected by this new global directive. It also only affects readers that are able to operate in both classic and enhanced geometry modes. If a reader only supports enhanced geometry or only supports classic geometry, then it is not affected by the parameter. In addition, the keyword does not guarantee that all features output by the reader will be enhanced (e.g., SHAPE); however wherever it is beneficial, enhanced geometry will be used. This is also true for some functions and factories as this directive does not tell the factory what type of geometry it should be outputting. Older workspaces/mapping files/FME Objects applications will continue to use classic geometry (for backwards compatibility).
For writers that support enhanced geometry, writing enhanced geometry is handled automatically. Features with either classic or enhanced geometry can be sent to the same writer. As long as the feature sent to the writer contained enhanced geometry, the writer will write the feature using enhanced geometry. In other words, to write enhanced geometry, you must have read enhanced geometry from a reader and routed it to the output. Or, you could have created enhanced geometry in one of the transformers that supports it (say by putting arcs and lines into a PolygonBuilder/PolygonFactory), and routing that output to the writer.
When the Geometry Handling parameter in Workbench is changed between Enhanced and Classic, some Readers and Transformers will change their behavior. If a Reader or Transformer's behavior is affected, this is noted in its documentation, either in the Transformer help, or in the FME Readers and Writers manual.
See the fmpedia article on the Geometry Model for more information on geometry handling.
For more information on the global directive that sets the usage of enhanced geometry in readers and writers (as well as functions, factories and transformers), see the FME Fundamentals on-line help, in FME Configuration > Geometry Handling. (The FME Fundamentals help is available as a link from the help menu.)