When you scan a card in Covve Scan, you have the option to add the card details as a new contact on your phone. Simply open a card you already scanned, tap on the blue (+) at the bottom right, and you should see the option to Save to phone.
For iPhone users, this will open the iPhone new contact dialog, and when you tap Done it will create a new contact on your phone. In case you have multiple contacts accounts on your phone (e.g. iCloud, Outlook, Google Contacts, etc.), and you want to save this card in a specific account, please make sure that you set that account as the default contacts account on your phone. To do this, go to your iPhone Settings -> Contacts -> Default Account
For Android users, this will open a dialog with all the available Contact Accounts on your phone, and you can select in which account you'd like the contact to be saved.