Lives are your attempts in game. A player can have no more than 5 lives. If you lose a level, you lose one life. You regain lives with time, one every 30 minutes.
The number of lives you have and the amount of time you have to wait to get your next one is displayed in the upper left corner near your avatar. You can also use rubies to regain a life.
You can also ask your Facebook friends to send you lives by tapping the Request Lives button. You can send lives to your friends using the corresponding button.