Uggner's unique unction is a spell that makes something one of a kind. It does this by destroying all other copies of the enchanted subject and prevent new ones from being created. Say you used this spell on a tree, it would destoy all other trees and prevent new ones from poping up. The only one that would survive is the one that you put the spell on making it one of a kind. Although the spell is more specific then that so it would destroy all other copies of that type of tree (say Maple or Oak). Snipe remarked that it was a simple enough spell for Barry to do it.
Barry almost used this spell to prevent there ever being a Barry Trotter movie.