Part of the anchor that allows rappelling/retreating without having to leave gear behind. Rappel rings are usually extended from the hanger via a chain but often you will find rings that go directly through the bolt. In other scenarios rappel rings may be attached with a webbing to a tree or rock tie-off.
Not every anchor necessarily has rappel rings. On many rock formations you may only find one anchor with rappel rings that usually follows the shortest or most convenient vertical way down the rock. Avoid being lowered off the rappel rings since it wears them out quickly. Always inspect your rappel rings before rigging and consider a rappel over a lower at all times.
In sport climbing it is a common technique to fiddle the rope through the rappel rings to then get lowered. This increases wear and tear on the rings through high fricition abuse. In many climbing areas this is not appropriate, especially where route maintenance is less likely to be done. Always inspect rings – a little more than 50% of original the ring diameter is generally respectable for use (if no other indicators raise concerns).