See the maya help to know about nonmainfold geometry.

To get ride of this kind of problem u can use Mesh > Cleanup.

For testing what is the result of cleanup is, u can set up a scene sth like this,

Create a plane with subdivisions width = 2 and subdivisions Height = 1.

Then grab the middle edge and extrude it.

then try to "reduce","subdivide" or anything that requires nonmainfold geometry to be removed.
.....
then use the cleanup to fix the object.
See the chance,
the extruded face has been separated from the main geometry though they are in the same object.

nonmainfold geometry is sth, that can't be stretched in a single plane.