A unique item is one of four specific objects required to complete the game:
Unique items versus artifacts
All artifacts are also unique within a game, but are not the same as unique items; they are specially named variants of their base item with additional benefits, and appear as named versions of those items when unidentified. The discoveries page lists identified artifacts under "Artifacts", whereas it lists unique items under "Unique Items".
While the unique items are also commonly referred to as invocation artifacts, they do not count as artifacts for wishing purposes, as the player is always guaranteed to encounter them.
Distinguishing from other "one-per-game" items
Most games will have no more than one runesword or tsurugi, by virtue of those items never generating randomly except when Stormbringer or the Tsurugi of Muramasa, respectively, are generated. Neither counts as a unique item; it is possible to wish for them or find them in a bones file (if the artifact already existed).
EvilHack adds a couple of other "one-per-game" items that serve as the base item for artifacts, and are never randomly generated (except when their associated artifact is generated):