A unique offer actually has to do with bonuses.
Each bonus will require a specific number of offers to be redeemed in order to earn the bonus. When you redeem a "unique offer" and purchase multiples, only the unique offer counts towards the bonus (not the multiples).
For example, if you redeem a Brand Name Yogurt offer and select the multiple of 3 on a single shopping trip, the offer will only count as ONE towards the bonus.
However, if you redeem a Brand Name Yogurt offer on one shopping trip, that will apply to a bonus; then, a few days later, the offer comes back and you redeem the Brand Name Yogurt offer on a different shopping trip, that will also apply to a bonus as a separate redemption.