Whoever says this unironically is usually a basic bitch who has nothing special about themselves. They often can't shut the fuck up about their "Uniqueness," when in reality they're an annoying, insecure, loser. Don't associate with them.
They could also be tell the truth, which is rare.
Stacy: "OMFG I'M SO QUIRKY AND UNIQUE!!!"
Bob: "Shut the actual fuck up."
Stacy: "But I'm unique! I deserve recognition and privilege for being special and different!"