You can upgrade any of the cards in your collection - Heroes, Weapons, Perks.

Once you've collected enough of a single card, and have enough coins to pay for it, tap on the card in your inventory and hit Upgrade/Train.

Upgrading a card makes it more powerful, allowing you to fight tougher battles. You also collect XP for upgrading cards which goes towards increasing your Player Level.

Once you have collected enough copies of a single card to fully upgrade it to the maximum level, you will receive Coins instead of more copies of that card. This allows you to continue to collect something useful, which you can use to upgrade more cards in your collection.