You are allowed to own a certain number of copies of each card. The maximum is calculated based on all the cards that are needed to upgrade that item, plus a little extra. Once you've reached this max amount, all extra cards you receive will be turned into Coins. The Coin value of a card depends on its rarity.

You can notice during a pack opening that some cards will show a golden gauge and a golden flag, stating how many copies were turned to Coins.

This will happens even if your card is not upgraded to the max level, but you have enough copies to do it.