Duplicate indexes are those that exactly match the Key and Included columns. That’s easy.
Possible duplicate indexes are those that very closely match Key/Included columns.
Why do you care?
Indexes have to be maintained. When I say that, most people immediately think of Reorganizing, rebuilding and updating statistics, and they are not wrong.
Click through for a great explanation of what “duplicate” indexes are, as well as ways to find them. If you’re searching for dupes, I’d recommend a couple blog posts from Kim Tripp as well on whether an index is really a duplicate and how to remove duplicate indexes.