To upgrade your weapons / armor you need Shadow Energy. You can do it in your inventory, just select an item that you want to upgrade and an icon will appear.

Each time when from chest / booster you get an item that you already have (same sword/helmet/etc.) instead of it you get a small amount of Shadow Energy.

Please note that cards with unique rarity (cards with a red border) can only be upgraded in the equipment section with special currency. Such special currency can be obtained from thematic events in the game, which are timed to one of the unique sets.