When you have someone `eating out of your hand’, you succeed in getting him to do whatever you want. The individual becomes very submissive.
*Within no time, the former film star had all the office employees eating out of her hand. *As a young man, he dreamed that he would have his wife eating out of his hand.
The expression comes from the world of animal training. You know that a wild animal has been tamed when you succeed in getting it to eat something off your hands, without getting bitten.