This will likely not be news to long-time Revit users, but after a couple of months of Revit use, I discovered this feature today. The project on which I am working has a number of pairs of identical patient rooms, which another team member set up as Model Groups. The rooms are arranged along the curved exterior of the building, so each group is rotated slightly from the adjacent groups. After working through several design iterations, I was trying to get the "final" design drawn accurately and to get the adjoining Walls to clean up correctly. I was frustrated by the lack of an exposed coordinate system or the equivalent of an insertion point in Revit. I also found it annoying that I had to continually repostition the rotation point when orienting each Model Group.
It turns out that there is an "origin" for Model Groups and that origin is the default rotation point for the group. Somewhere along the line, the origin of our Model Group got moved off to a random point within one of the rooms. Fortunately, it is quite easy to relocate the origin point. (Which probably explains how it got moved to such a strange place - it is almost too easy to move it.) Simply select an instance of the Model Group in a Plan or 3D view. As shown in the image below, in a Plan view you will get two axes, labeled "X" and "Y", with three grip points. Click on the grip point at the intersection of the axes......and drag the grip......to the point where you want the origin placed and release the left mouse button.I used an intersection snap [SI] in the example in the screen captures to be certain it was placed accurately. The grips at the "arrow ends" of the axes allow you to rotate the axes, if you want to change the angle at which the Model Group initially inserts.
One small step on the road to Revit enlightenment; one giant reduction in frustration.