John,
This looks like some version of a "knob guard", possibly home-made. These are typically installed on gates where it is possible to reach through the gate opening from the outside to operate the knob or lever. If you install a knob guard, it makes it a little harder to reach over or through the gate to grab the knob. Unless your door is right next to a gate or fence, I don't think that this is the purpose of the guard here however.
A fairly common burglary technique is to use a large pipe wrench on cylindrical locks such as these. This creates a tremendous amount of torque on the lock body and the door usually pops right open. I suppose that this ring would proviode some degree of protection against this type of attack.