The ear piece gives them timing cues. It can be used to play a song or parts of a song that they may not remember. Mostly its so they know whats happening. Monitors, the big speakers they have facing them are there so they can hear what they are singing, playing, etc.
They use the earpiece to listen to themselves singing. The device also helps them to see whether they are on key or not. A moderate amount of ambient noise can also prevent the singers from hearing themselves well enough to know whether they are on key or not.
That is correct but the other reason is when the singers are on stage, and live music is played, there is a slight delay or rebound for the singers to hear the music being played because of the sound bounce from the farthest wall and can confuse the singers timing. That's why sometimes at ball games, the singer singing the anthem gets lost.