Boosters are packs of card pieces. In a way, the booster is a bit like a game. You will been shown 8 cards, and you'll be allowed to flip over four of them for free (you can see a list of what is hidden under them on the right).
You can flip additional cards for premium currency. Once you're done, just click on the "Redeem" button.
Boosters come in Bronze, Silver and Gold qualities. The higher the quality, the higher the chances of getting rare and valuable cards. You will receive a free Bronze booster every day!