To have something 'in the palm of your hand' means to have influence or control over it. If you have an audience 'in the palm of your hand' you have a captive audience who are relating to what you are saying and hanging on every word. Someone who has the power to make a decision might have someone's fate 'in the palm of their hand'. This is an idiom used in both social and professional contexts.

1. John's performance was excellent. He had the audience eating out of the palm of his hand. 
2. The professor who can decide your final grade literally has your future in the palm of their hand.

1. I think Anne has too much power in the company. She has the Board in the palm of her hand.
2. My sales pitch was sharp and to the point, so I managed to keep the investors in the palm of my hand throughout.