If you are politic, you are smooth and diplomatic. You'd probably make a good politician.
Being politic is being polite and agreeable. Screaming and yelling is not politic. Speaking quietly, making apologies, and giving compliments are all politic things to do. When you want something, being politic is the way to go. It can definitely help to remember that politicians are good at getting what they want — they are shrewd and very politic.