At the start of the game, Caligula gets 2 secret Privilege cards, while the other players get one card. A privilege acts like a joker and allows a twist in the distribution of cards.
With the Special gift card, you can force a player to accept the Gift card.
With the Give back card, you force a player to accept the Gift card that he wants to give away.
With the Claim card, you can claim one card, i.e. keep or gift the gift card.
With the Exchange card, you can exchange 2 cards, i.e. keep with discard card.
When you use your privilege card, you must discard it.
Therefore, keeping your privilege as long as possible, can be a wise tactical option. The threat of playing a privilege is sometimes more powerful than using it.