To jawbone is to talk informally. Think "schmooze," "talk up," or "chit chat;" it's a word to use when the act of talking is more important than what's being talked about.
In a financial or political context, jawboning is a form of persuasion. When Lyndon B. Johnson attempted to jawbone rising interest-rates in 1966, he was attempting to change the behavior of the markets without taking direct action. Franklin D. Roosevelt's Fireside Chats can be seen as jawboning as well, as FDR enlisted support first for New Deal programs and then for the US role in World War II through informal, friendly radio-broadcast "chats."