From Photography Wiki
Adapter rings are used to mount accessories like filters on lenses with the wrong filter thread size.
Two categories are available:
- step up rings to adapt a large filter on a smaller lens
- step down rings to adapt a smaller filter on a larger lens (this will most of the time cause some vignetting)
The advantage is to be able to use a single filter (for instance a 77mm polarizer) on different types of lenses.