Simply put, the difference is primarily that of legitimacy. Power is usually broadly defined as the ability to influence people or events. Authority, on the other hand, refers to the legally, morally, or socially accepted right to exercise power. For example, an individual might have the power to punish someone for committing an offense against them. But only the state, in the form of law enforcement and the courts, would have the authority to do so. A nation might have the power to invade and conquer another nation, but would only have the authority to do so in its own defense or with the sanction of the international community. So authority is perhaps best thought of as legitimately exercised power. It should be noted, however, that one's legitimacy, i.e. their authority, can be contested, because people will not always recognize its basis.