Common cards are, as the name implies, the most common cards in the game and by default you have an 80% chance to pull a common card. They are depicted in-game with a white-colored frame.
When buying cards, the rarity is chosen first then a card is selected within that rarity. The chance of getting each rarity is: Common: 80%, Rare Cards: 17%, Epic Cards: 3%.
Once all common cards have been bought, the chance to buy Rare Cards becomes 97%. And once all cards are acquired, you get the chance to unlock Card Mastery.