This is to help you manage patrons you've sent rewards to.
If you're sending rewards via your patron manager, you can individually select patrons and mark them complete. You can select "Completed Patrons" and see all the patrons you've already fulfilled rewards to.
Don't worry--marking patrons complete does not remove them from your list of patrons! This is simply a visual way for you to see which patrons you have/haven't send rewards to yet.