The little green leaf at the top left corner of some cards indicates that the card is permanently safe in your Pack and cannot be stolen by other players or the Rats. The main exception is if this card is then traded to another player; the card will lose the leaf lock and permanent safety once traded.
The vast majority of cards with the leaf on it have been purchased with tickets, and so they usually have a gold border as well:
But, some cards in PackRat will have the leaf, but no gold border; such cards are found in the starter Packs given to players when they first sign up to play:
However, such a card CAN still be Vaulted, traded, or combined into a recipe card. To prevent this from accidentally happening to a card in your Pack you really love, you can make that card your Pack Pet with a Pack Pet Lock, and it will be safe from any movement or transactions unless you decide to remove the lock!