If she does have a listening device in her ear, it is because these have replaced the old-time monitors, the backwards speakers that let the musicians on stage hear what sounds they are making. Trust me, when you are playing electrified instruments and signing through a microphone it is really, really hard to hear what you yourself are doing. The in-ear device lets you hear what you need to in order to sing or play your best.
If she doesn’t have something in her ear, then it would most likely be as others have said, to better hear herself so she is on key, on pitch and on time. As to the hand waving, yes, it is taught to aspiring singers to help them conceptualize the pitch they are striving to reach, and yes, most professionally-trained singers are discouraged from using the hand gestures on stage, but I don’t know how much vocal training Cary has had or whether she discovered for herself that it helps.
In any case, some people like the way she sings or she wouldn’t sell so many records, and if sticking a finger in her ear or waving a hand around allows her to produce the sounds her fans like, then more power to her.
And, at the moment, I can’t remember what she sounds like at all, although I am sure I must have heard something by her sometime.