Here's one for those who've been around the block a few times.
ArcInfo Workstation from days of yore had an intelligent data model called Regions or Region sub coverages. With this model one could select one or more polygons and create new virtual polygons from the selected set. Furthermore one could dissolve within the set, creating a result akin to merged polygons, or have disparate polygons, possibly overlapping, that identify themselves as one unit (multipart polygons in shapefile parlance). These virtual polygons are called regions. When the regions are loaded into Arcmap (or ArcEdit/View back then) they behave like an independent shapefile or feature class in terms of querying, symbolizing, etc.
The beauty of this model and what is missing from feature classes and feature datasets in the ArcGIS world, so far as I've been able to determine, is that in regions the geometry is stored only once. Imagine, for example, the continent of North America split into polygons depicting countries, islands, states & territories, counties, municipalities, etc. down to whatever level you feel like stopping at, all stored in a single feature class. (ugh, what a mess) Yet, each level has convenient handles (country, province, whatever) that can be grabbed and used as if they were independent feature classes.
Coverages and Regions have their problems, they weren't left behind lightly, but they weren't all bad. Sooo, what is the ArcGIS answer to ArcInfo Regions?
Answer
I'm one of those lucky ones (I think) that entered the GIS world at about the time coverages were being phased out. I've used them, and still do sometimes, but never had to deal with thm in the old pre-ArcGIS ArcInfo.
To answer your question as simply as possible, I don't believe there is anything comparable to Regions or Region sub covrages in the new geodatabase model.
Here's a link to a white paper from 2003 describing the differences between coverages and geodtabases: ArcGIS: Working With Geodatabase Topology
From what I've gleened from this paper, ESRI believed at that time that any benefits from th efficiency of the coverage model were not enough to continue supporting it. Thus the move to the more flexible geodatabase.
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