The Hearts are tokens you can earn by watching videos in advance, or by completing the Golden Deck achievements.
Just tap the Heart icon in the top-right of the home screen, and you'll have an option to watch videos to earn extra hearts.
Each token gives you an ad-free deal of any game you choose. Some games are longer than others, but they all cost just one token.
The Golden Deck cards each award you extra hearts, so it is worth collecting them and unlocking any you can!
On the Hearts page there is the option to Watch a Video. This is a short advert video or promotion - usually about 15-30 seconds long. At the end you'll usually get the choice to follow a link (a download of another app, perhaps), or you can return back to the Hearts page by pressing the 'X' to close the video, which will be in the corner of the screen. On some screens this can be a bit small (we're sorry - it's out of our direct control!) so tap carefully in the corner.
Video Ads earn you 5 hearts for each one that you complete watching. If you skip out of the video (there is often the option to do so), then you won't get any hearts at the end.
If you run out of Hearts
If you don't have any hearts left, the next time you start a new deal, you'll have the option to watch an ad in advance before starting the game. You won't necessarily get an advert every time, though - so some of your plays will still be ad-free!