It's mostly there to help a singer hear their own song. It's like a cue so that they can hear themselves, since the stage and music often prevents an artist from hearing their own voice through their performance.
Almost like a feedback for them to use, to keep on pitch and rythym. I also agree with w_z in that sometimes your head voice is better. The ear monitors are very loud too, so it might overbear their ears too.
This is also why at concert or live, artists sometimes sound very different from their cd's, especially if they don't use these things.
Why she took her's out, I don't know, but it's probably for one of the above reasons.
These are also used in the news by casters, in those it is actually a person, feeding the words to the news broadcaster, cuing them on what to include and say.
I know that because my cousin was a newscaster for a local station. She isn't a reporter anymore, but she does still consult with them sometimes Great question though!
~Amanda